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ADJOINT BUNDLE

  • Adjoint bundle
  • mathematics, an adjoint bundle is a vector bundle naturally associated with any smooth principal bundle. The fibers of the adjoint bundle carry a Lie algebra

    Adjoint bundle

    Adjoint_bundle

  • Lie algebra–valued differential form
  • with any tensorial forms on P {\displaystyle P} of adjoint type. Maurer–Cartan form Adjoint bundle S. Kobayashi, K. Nomizu. Foundations of Differential

    Lie algebra–valued differential form

    Lie_algebra–valued_differential_form

  • Gauge theory (mathematics)
  • Study of vector bundles, principal bundles, and fibre bundles

    The Lie algebra adjoint bundle is usually denoted ad ⁡ ( P ) {\displaystyle \operatorname {ad} (P)} , and the Lie group adjoint bundle by Ad ⁡ ( P ) {\displaystyle

    Gauge theory (mathematics)

    Gauge_theory_(mathematics)

  • Adjoint representation
  • Mathematical term

    In mathematics, the adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations

    Adjoint representation

    Adjoint representation

    Adjoint_representation

  • Connection (principal bundle)
  • Concept in mathematics

    section of the vertical bundle V of P. Hence it is basic and so is determined by a 1-form on M with values in the adjoint bundle g P := P × G g . {\displaystyle

    Connection (principal bundle)

    Connection_(principal_bundle)

  • Yang–Mills equations
  • Partial differential equations whose solutions are instantons

    bundle. This connection has a curvature form F A {\displaystyle F_{A}} , which is a two-form on X {\displaystyle X} with values in the adjoint bundle

    Yang–Mills equations

    Yang–Mills equations

    Yang–Mills_equations

  • Monopole
  • Topics referred to by the same term

    (mathematics), a connection over a principal bundle G with a section (the Higgs field) of the associated adjoint bundle Monopole, the first term in a multipole

    Monopole

    Monopole

  • Connection (vector bundle)
  • Defines a notion of parallel transport on a bundle

    capital A adjoint bundle Ad ⁡ ( F ( E ) ) {\displaystyle \operatorname {Ad} ({\mathcal {F}}(E))} of the frame bundle of the vector bundle E {\displaystyle

    Connection (vector bundle)

    Connection_(vector_bundle)

  • Differential operator
  • Typically linear operator defined in terms of differentiation of functions

    self-adjoint operator is an operator equal to its own (formal) adjoint. If Ω is a domain in Rn, and P a differential operator on Ω, then the adjoint of

    Differential operator

    Differential operator

    Differential_operator

  • Gluon field strength tensor
  • Second-rank tensor in quantum chromodynamics

    field on the spacetime with values in the adjoint bundle of the chromodynamical SU(3) gauge group (see vector bundle for necessary definitions). Throughout

    Gluon field strength tensor

    Gluon field strength tensor

    Gluon_field_strength_tensor

  • Yang–Mills–Higgs equations
  • Yang–Mills coupled to a Higgs field

    connection, and a Higgs field, given by a section of a vector bundle (specifically, the adjoint bundle). These equations are D A ∗ F A + ∗ [ Φ , D A Φ ] = 0

    Yang–Mills–Higgs equations

    Yang–Mills–Higgs_equations

  • Bogomolny equations
  • Equations describing magnetic monopoles

    {\displaystyle G} -bundle over a 3-manifold M {\displaystyle M} , Φ {\displaystyle \Phi } is a section of the corresponding adjoint bundle, d A {\displaystyle

    Bogomolny equations

    Bogomolny_equations

  • Stable principal bundle
  • {C} )} there is still a natural associated vector bundle to P {\displaystyle P} , the adjoint bundle ad ⁡ P {\displaystyle \operatorname {ad} P} , with

    Stable principal bundle

    Stable_principal_bundle

  • Adjoint functors
  • Relationship between two functors abstracting many common constructions

    this relationship are known as adjoint functors, one being the left adjoint and the other the right adjoint. Pairs of adjoint functors are ubiquitous in mathematics

    Adjoint functors

    Adjoint_functors

  • Monopole (mathematics)
  • mathematics, a monopole is a connection over a principal bundle G with a section of the associated adjoint bundle. Physically, such a monopole can be interpreted

    Monopole (mathematics)

    Monopole_(mathematics)

  • G-structure on a manifold
  • Structure group sub-bundle on a tangent frame bundle

    difference of two adapted connections is a 1-form on M with values in the adjoint bundle AdQ. That is to say, the space AQ of adapted connections is an affine

    G-structure on a manifold

    G-structure_on_a_manifold

  • Principal SU(2)-bundle
  • Special type of principal bundle

    Unlike the associated vector bundle, a complex plane bundle, the adjoint vector bundle is a orientable real vector bundle of third rank. Also since SU

    Principal SU(2)-bundle

    Principal_SU(2)-bundle

  • Lie algebra bundle
  • Concept in topology (mathematics)

    Lie group bundle over the same base space whose Lie algebra bundle is isomorphic to the given Lie algebra bundle. Algebra bundle Adjoint bundle A. Weinstein

    Lie algebra bundle

    Lie_algebra_bundle

  • Affine space
  • Euclidean space without distance and angles

    1-forms, where ad ( P ) {\displaystyle {\text{ad}}(P)} is the associated adjoint bundle. For any non-empty subset X of an affine space A, there is a smallest

    Affine space

    Affine space

    Affine_space

  • Hitchin's equations
  • System of partial differential equations used in Higgs field theory

    {\displaystyle {\text{ad}}P^{\mathbb {C} }} is the complexification of the adjoint bundle of P {\displaystyle P} , with fibre given by the complexification g

    Hitchin's equations

    Hitchin's_equations

  • Principal U(1)-bundle
  • Special type of principal bundle

    Principal bundles also have an adjoint vector bundle, which is trivial for principal U ⁡ ( 1 ) {\displaystyle \operatorname {U} (1)} -bundles. By definition

    Principal U(1)-bundle

    Principal U(1)-bundle

    Principal_U(1)-bundle

  • Weitzenböck identity
  • Relates 2 second-order elliptic operators on a manifold with the same principal symbol

    are implemented for G-invariant self-adjoint operators between vector bundles associated to some principal G-bundle, although the precise conditions under

    Weitzenböck identity

    Weitzenböck_identity

  • Vertical and horizontal bundles
  • Mathematics concept

    vertical bundle and the horizontal bundle are vector bundles associated to a smooth fiber bundle. More precisely, given a smooth fiber bundle π : E → B

    Vertical and horizontal bundles

    Vertical and horizontal bundles

    Vertical_and_horizontal_bundles

  • Gauge group (mathematics)
  • Group of gauge symmetries in Yang–Mills theory

    Yang–Mills gauge theory of principal connections on a principal bundle. Given a principal bundle P → X {\displaystyle P\to X} with a structure Lie group G {\displaystyle

    Gauge group (mathematics)

    Gauge_group_(mathematics)

  • Lie algebroid
  • Infinitesimal version of Lie groupoid

    on P {\displaystyle P} , its isotropy Lie algebra bundle is isomorphic to the adjoint vector bundle P × G g {\displaystyle P\times _{G}{\mathfrak {g}}}

    Lie algebroid

    Lie_algebroid

  • Yang–Mills–Higgs flow
  • Gradient flow of the Yang–Mills–Higgs action functional

    \operatorname {Ad} (E):=E\times _{G}{\mathfrak {g}}\twoheadrightarrow B} be its adjoint bundle. A = Ω Ad 1 ( E , g ) {\displaystyle {\mathcal {A}}=\Omega _{\operatorname

    Yang–Mills–Higgs flow

    Yang–Mills–Higgs flow

    Yang–Mills–Higgs_flow

  • Transpose
  • Matrix operation which flips a matrix over its diagonal

    resulting in an isomorphism between the transpose and adjoint of u. The matrix of the adjoint of a map is the transposed matrix only if the bases are

    Transpose

    Transpose

    Transpose

  • Fujita conjecture
  • MR 1207013. Fujita, Takao (1987), "On polarized manifolds whose adjoint bundles are not semipositive", Algebraic geometry, Sendai, 1985, Adv. Stud

    Fujita conjecture

    Fujita_conjecture

  • Yang–Mills flow
  • Gradient flow of the Yang–Mills action functional

    \operatorname {Ad} (E):=E\times _{G}{\mathfrak {g}}\twoheadrightarrow B} be its adjoint bundle. A = Ω Ad 1 ( E , g ) {\displaystyle {\mathcal {A}}=\Omega _{\operatorname

    Yang–Mills flow

    Yang–Mills flow

    Yang–Mills_flow

  • Lichnerowicz formula
  • Formula for spinors

    is the self-dual part of the curvature of A. The asterisks denote the adjoint of the quantity and the brackets ⟨ , ⟩ {\displaystyle \langle ,\rangle

    Lichnerowicz formula

    Lichnerowicz_formula

  • Laplace operators in differential geometry
  • Elliptic differential operators in geometry mathematics

    sections of E, and T*M is the cotangent bundle of M. It is possible to take the L 2 {\displaystyle L^{2}} -adjoint of ∇ {\displaystyle \nabla } , giving

    Laplace operators in differential geometry

    Laplace_operators_in_differential_geometry

  • Holonomy
  • Concept in differential geometry

    holonomy of connections in vector bundles, holonomy of Cartan connections, and holonomy of connections in principal bundles. In each of these cases, the holonomy

    Holonomy

    Holonomy

    Holonomy

  • Pullback
  • Process in mathematics

    linear operator, and is known as the transpose or composition operator. Its adjoint is the push-forward, or, in the context of functional analysis, the transfer

    Pullback

    Pullback

  • Seiberg–Witten flow
  • Gradient flow of the Seiberg–Witten action functional

    _{\operatorname {U} (1)}\mathbb {C} } using the balanced product and with trivial adjoint bundle Ad ⁡ Fr U ⁡ ( L ) ≅ End _ ( L ) ≅ C _ {\displaystyle \operatorname {Ad}

    Seiberg–Witten flow

    Seiberg–Witten flow

    Seiberg–Witten_flow

  • Vector-valued differential form
  • of adjoint type. The "difference" of two connection forms is a tensorial form. Given P and ρ as above one can construct the associated vector bundle E

    Vector-valued differential form

    Vector-valued_differential_form

  • Atiyah–Singer index theorem
  • Mathematical result in differential geometry

    the operators of the elliptic complex and their adjoints, restricted to the sum of the even bundles. If the manifold is allowed to have boundary, then

    Atiyah–Singer index theorem

    Atiyah–Singer_index_theorem

  • Projective unitary group
  • Quotient of special unitary group by its center

    of PU. The adjoint action of the infinite projective unitary group is useful in geometric definitions of twisted K-theory. Here the adjoint action of the

    Projective unitary group

    Projective_unitary_group

  • Fundamental groupoid
  • category (while the fundamental groupoid is a left adjoint to the inclusion of Gprd, the core is a right adjoint) Brown, Ronald (2006). Topology and Groupoids

    Fundamental groupoid

    Fundamental_groupoid

  • Connection form
  • Math/physics concept

    right action on T(FGE) with the adjoint representation of G. Conversely, a principal G-connection ω in a principal G-bundle P→M gives rise to a collection

    Connection form

    Connection_form

  • Reflective subcategory
  • Concept in mathematical theory of categories

    reflective in B when the inclusion functor from A to B has a left adjoint. This adjoint is sometimes called a reflector, or localization. Dually, A is said

    Reflective subcategory

    Reflective_subcategory

  • Normal
  • Topics referred to by the same term

    of digits Normal operator, an operator that commutes with its Hermitian adjoint Normal order of an arithmetic function, a type of asymptotic behavior useful

    Normal

    Normal

  • Yang–Mills moduli space
  • Moduli space of the Yang–Mills equations

    {\displaystyle \operatorname {Ad} (P):=P\times _{G}{\mathfrak {g}}} be the adjoint bundle, then the Yang–Mills equations as well as the (anti) self-dual Yang–Mills

    Yang–Mills moduli space

    Yang–Mills_moduli_space

  • Chern–Simons theory
  • Topological quantum field theory

    flat G-principal bundle P on M there exists a unique homomorphism, called the Chern–Weil homomorphism, from the algebra of G-adjoint invariant polynomials

    Chern–Simons theory

    Chern–Simons_theory

  • Representable functor
  • Functor type

    representable if and only if it has a left adjoint. The categorical notions of universal morphisms and adjoint functors can both be expressed using representable

    Representable functor

    Representable_functor

  • Bott periodicity theorem
  • Describes a periodicity in the homotopy groups of classical groups

    {\displaystyle \Omega } is the loop space functor, right adjoint to suspension and left adjoint to the classifying space construction. Bott periodicity

    Bott periodicity theorem

    Bott_periodicity_theorem

  • List of things named after Charles Hermite
  • given magnitude Einstein–Hermitian vector bundle Deformed Hermitian Yang–Mills equation Hermitian adjoint Hermitian connection, the unique connection

    List of things named after Charles Hermite

    List_of_things_named_after_Charles_Hermite

  • F-Yang–Mills equations
  • \operatorname {Ad} (E):=E\times _{G}{\mathfrak {g}}\twoheadrightarrow B} be its adjoint bundle. Ω Ad 1 ( E , g ) ≅ Ω 1 ( B , Ad ⁡ ( E ) ) {\displaystyle \Omega _{\operatorname

    F-Yang–Mills equations

    F-Yang–Mills_equations

  • Functor
  • Mapping between categories

    be proved by realizing that it is the right-adjoint to the diagonal functor and invoking the Freyd adjoint functor theorem. This requires a suitable version

    Functor

    Functor

  • Cone (algebraic geometry)
  • Generalization of a vector bundle

    In algebraic geometry, a cone is a generalization of a vector bundle. Specifically, given a scheme X, the relative Spec C = Spec X ⁡ R {\displaystyle C=\operatorname

    Cone (algebraic geometry)

    Cone_(algebraic_geometry)

  • Ehresmann connection
  • Differential geometry construct on fiber bundles

    on any smooth fiber bundle. In particular, it does not rely on the possible vector bundle structure of the underlying fiber bundle, but nevertheless, linear

    Ehresmann connection

    Ehresmann_connection

  • Bi-Yang–Mills equations
  • \operatorname {Ad} (E):=E\times _{G}{\mathfrak {g}}\twoheadrightarrow B} be its adjoint bundle. Ω Ad 1 ( E , g ) ≅ Ω 1 ( B , Ad ⁡ ( E ) ) {\displaystyle \Omega _{\operatorname

    Bi-Yang–Mills equations

    Bi-Yang–Mills_equations

  • Lift (mathematics)
  • topology and homological algebra, tensor product and the Hom functor are adjoint; however, they might not always lift to an exact sequence. This leads to

    Lift (mathematics)

    Lift_(mathematics)

  • Stable Yang–Mills–Higgs pair
  • Concept in differential geometry

    {\displaystyle \operatorname {Ad} (E):=E\times _{G}{\mathfrak {g}}} be its adjoint bundle. A = Ω Ad 1 ( E , g ) {\displaystyle {\mathcal {A}}=\Omega _{\operatorname

    Stable Yang–Mills–Higgs pair

    Stable_Yang–Mills–Higgs_pair

  • Tensor algebra
  • Universal construction in multilinear algebra

    tensor product. It is the free algebra on V, in the sense of being left adjoint to the forgetful functor from algebras to vector spaces: it is the "most

    Tensor algebra

    Tensor_algebra

  • Serre duality
  • Theorem in algebraic geometry

    varieties, proved by Jean-Pierre Serre. The basic version applies to vector bundles on a smooth projective variety, but Alexander Grothendieck found wide generalizations

    Serre duality

    Serre_duality

  • Laplace–Beltrami operator
  • Operator generalizing the Laplacian in differential geometry

    consequence, the Laplace–Beltrami operator is negative and formally self-adjoint, meaning that for compactly supported functions f {\displaystyle f} and

    Laplace–Beltrami operator

    Laplace–Beltrami_operator

  • Stable Yang–Mills connection
  • Concept in differential geometry

    {\displaystyle \operatorname {Ad} (E):=E\times _{G}{\mathfrak {g}}} be its adjoint bundle. A = Ω Ad 1 ( E , g ) {\displaystyle {\mathcal {A}}=\Omega _{\operatorname

    Stable Yang–Mills connection

    Stable_Yang–Mills_connection

  • Dirac operator
  • First-order differential linear operator on spinor bundle, whose square is the Laplacian

    space of smooth, square-integrable functions. It can be extended to a self-adjoint operator on that domain. The square, in this case, is not the Laplacian

    Dirac operator

    Dirac_operator

  • Atiyah algebroid
  • G} , its quotient by the diagonal G {\displaystyle G} action is the adjoint bundle P × G g {\displaystyle P\times _{G}{\mathfrak {g}}} . In conclusion

    Atiyah algebroid

    Atiyah_algebroid

  • Pullback (category theory)
  • Most general completion of a commutative square given two morphisms with same codomain

    maps) X ×B E is a fiber bundle over X called the pullback bundle. The associated commutative diagram is a morphism of fiber bundles. A special case is the

    Pullback (category theory)

    Pullback_(category_theory)

  • K-theory
  • Branch of mathematics

    K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is a cohomology

    K-theory

    K-theory

  • Special unitary group
  • Group of unitary complex matrices with determinant of 1

    Tr(T_{a}T_{b})={\frac {1}{2}}\delta _{ab}.} In the (n2 − 1)-dimensional adjoint representation, the generators are represented by (n2 − 1) × (n2 − 1) matrices

    Special unitary group

    Special unitary group

    Special_unitary_group

  • Tensor product of modules
  • Operation that pairs a left and a right R-module into an abelian group

    _{S}P=M\otimes _{R}(N\otimes _{S}P)} as abelian group. The general form of adjoint relation of tensor products says: if R is not necessarily commutative,

    Tensor product of modules

    Tensor_product_of_modules

  • Dirac equation
  • Relativistic quantum mechanical wave equation

    }^{a}} , formally the connection on the principal bundle, which necessarily transforms in the adjoint representation of the gauge group. The covariant

    Dirac equation

    Dirac_equation

  • Hitchin system
  • Type of integrable system

    system is a partial compactification of the cotangent bundle to the moduli space of stable G-bundles for some reductive group G, on some compact algebraic

    Hitchin system

    Hitchin_system

  • Connection (fibred manifold)
  • Operation on fibered manifolds

    acts on by the adjoint representation. There is the canonical imbedding of C to the quotient bundle TP/G which also is called the bundle of principal connections

    Connection (fibred manifold)

    Connection_(fibred_manifold)

  • Ginzburg–Landau theory
  • Superconductivity theory

    {Re} \langle D\psi ,\psi \rangle } where D ∗ {\displaystyle D^{*}} is the adjoint of D {\displaystyle D} , analogous to the codifferential δ = d ∗ {\displaystyle

    Ginzburg–Landau theory

    Ginzburg–Landau_theory

  • Homotopy theory
  • Branch of mathematics

    product X ∧ Y {\displaystyle X\wedge Y} which is characterized by the adjoint relation Map ⁡ ( X ∧ Y , Z ) = Map ⁡ ( X , Map ⁡ ( Y , Z ) ) {\displaystyle

    Homotopy theory

    Homotopy_theory

  • Lie algebra cohomology
  • Cohomology theory for Lie algebras

    here. When M = g {\displaystyle M={\mathfrak {g}}} , the action is the adjoint action, x ⋅ y = [ x , y ] = ad ( x ) y {\displaystyle x\cdot y=[x,y]={\text{ad}}(x)y}

    Lie algebra cohomology

    Lie_algebra_cohomology

  • Chern–Weil homomorphism
  • Mathematical theory

    points in C [ g ] {\displaystyle \mathbb {C} [{\mathfrak {g}}]} under the adjoint action of G; that is, the subalgebra consisting of all polynomials f such

    Chern–Weil homomorphism

    Chern–Weil_homomorphism

  • Quadratic Lie algebra
  • symmetric bilinear form. Compatibility means that it is invariant under the adjoint representation. Examples of such are semisimple Lie algebras, such as su(n)

    Quadratic Lie algebra

    Quadratic Lie algebra

    Quadratic_Lie_algebra

  • Complexification (Lie group)
  • Universal construction of a complex Lie group from a real Lie group

    iX, where u is a unitary operator in the compact group and X is a skew-adjoint operator in its Lie algebra. In this case the complexification is a complex

    Complexification (Lie group)

    Complexification (Lie group)

    Complexification_(Lie_group)

  • Riemannian connection on a surface
  • Intrinsic geometric structures in mathematics

    trivial bundle, in particular to a section of the original sub-bundle, although the resulting section might no longer be a section of the sub-bundle. This

    Riemannian connection on a surface

    Riemannian_connection_on_a_surface

  • Spectral triple
  • involves a Hilbert space, an algebra of operators on it and an unbounded self-adjoint operator, endowed with supplemental structures. It was conceived by Alain

    Spectral triple

    Spectral_triple

  • Fibred category
  • Concept in category theory

    objects such as vector bundles can be defined. As an example, for each topological space there is the category of vector bundles on the space, and for

    Fibred category

    Fibred_category

  • Lie group–Lie algebra correspondence
  • Correspondence between topics in Lie theory

    category of finite-dimensional (real) Lie-algebras. This functor has a left adjoint functor Γ {\displaystyle \Gamma } from (finite dimensional) Lie algebras

    Lie group–Lie algebra correspondence

    Lie_group–Lie_algebra_correspondence

  • Hodge star operator
  • Exterior algebraic map taking tensors from p forms to n-p forms

    cotangent bundle of a pseudo-Riemannian manifold, and hence to differential k-forms. This allows the definition of the codifferential as the Hodge adjoint of

    Hodge star operator

    Hodge_star_operator

  • Maurer–Cartan form
  • Mathematical concept

    pullback of forms along the right-translation in the group and Ad(h) is the adjoint action on the Lie algebra. If X is a left-invariant vector field on G,

    Maurer–Cartan form

    Maurer–Cartan_form

  • Kähler manifold
  • Manifold with Riemannian, complex and symplectic structure

    Lefschetz operator L := ω ∧ − {\displaystyle L:=\omega \wedge -} and its adjoint, the contraction operator Λ = L ∗ {\displaystyle \Lambda =L^{*}} . The

    Kähler manifold

    Kähler_manifold

  • Solvmanifold
  • (X)\colon {\mathfrak {g}}\to {\mathfrak {g}},X\in {\mathfrak {g}}} in its adjoint representation is hyperbolic, i.e., it has only real eigenvalues. Let G

    Solvmanifold

    Solvmanifold

  • Kähler identities
  • operators on a Kähler manifold relating the Dolbeault operators and their adjoints, contraction and wedge operators of the Kähler form, and the Laplacians

    Kähler identities

    Kähler_identities

  • Noncommutative geometry
  • Branch of mathematics

    Hilbert space H {\displaystyle H} , together with a usually unbounded self-adjoint operator D {\displaystyle D} , such that ( 1 + D 2 ) − 1 / 2 {\displaystyle

    Noncommutative geometry

    Noncommutative_geometry

  • List of mathematical topics in quantum theory
  • entanglement spinor, spinor group, spinor bundle Dirac sea Spin foam Poincaré group gamma matrices Dirac adjoint Wigner's classification anyon Copenhagen

    List of mathematical topics in quantum theory

    List_of_mathematical_topics_in_quantum_theory

  • Hilbert C*-module
  • Mathematical objects that generalise the notion of Hilbert spaces

    a C*-algebra A {\displaystyle A} is said to be positive if it is self-adjoint with non-negative spectrum.) An analogue to the Cauchy–Schwarz inequality

    Hilbert C*-module

    Hilbert_C*-module

  • Gorenstein ring
  • Local ring in commutative algebra

    simply a line bundle (viewed as a complex in degree −dim(X)); this line bundle is called the canonical bundle of X. Using the canonical bundle, Serre duality

    Gorenstein ring

    Gorenstein_ring

  • SL2(R)
  • Group of real 2×2 matrices with unit determinant

    PSL(2, R) can be described as the unit tangent bundle of the hyperbolic plane. It is a circle bundle, and has a natural contact structure induced by

    SL2(R)

    SL2(R)

    SL2(R)

  • Stack (mathematics)
  • Generalisation of a sheaf; a fibered category that admits effective descent

    situations where isomorphic, compatible geometrical objects (such as vector bundles on topological spaces) can be "glued together" within a restriction of

    Stack (mathematics)

    Stack_(mathematics)

  • Tensor product
  • Mathematical operation on vector spaces

    (U,\mathrm {Hom} (V,W)).} This is an example of adjoint functors: the tensor product is "left adjoint" to Hom. The tensor product of two modules A and

    Tensor product

    Tensor_product

  • ∞-Chern–Weil theory
  • Combination of higher category theory with Chern–Weil theory

    \colon \mathbf {H} \rightarrow \infty \operatorname {Grpd} } has a right adjoint Disc : ∞ Grpd → H {\displaystyle \operatorname {Disc} \colon \infty \operatorname

    ∞-Chern–Weil theory

    ∞-Chern–Weil_theory

  • Orthogonal matrix
  • Real square matrix whose columns and rows are orthogonal unit vectors

    (with inverse Q−1 = QT), unitary (Q−1 = Q∗), where Q∗ is the Hermitian adjoint (conjugate transpose) of Q, and therefore normal (Q∗Q = QQ∗) over the real

    Orthogonal matrix

    Orthogonal_matrix

  • Lie group action
  • {\displaystyle G} by left multiplication, right multiplication or conjugation; the adjoint action of G {\displaystyle G} on its Lie algebra g {\displaystyle {\mathfrak

    Lie group action

    Lie_group_action

  • Transversality
  • Description of how spaces intersect in mathematics

    [{\mathfrak {g}},e]} is the tangent space at e {\displaystyle e} to the adjoint orbit A d ( G ) e {\displaystyle {\rm {{Ad}(G)e}}} and so the affine space

    Transversality

    Transversality

  • Coherent duality
  • Generalisations of Serre duality in mathematics

    'local' theory. The historical roots of the theory lie in the idea of the adjoint linear system of a linear system of divisors in classical algebraic geometry

    Coherent duality

    Coherent_duality

  • Differential form
  • Expression that may be integrated over a region

    \Omega ^{k}(M)\rightarrow \Omega ^{k-1}(M)} , which has degree −1 and is adjoint to the exterior differential d. On a pseudo-Riemannian manifold, 1-forms

    Differential form

    Differential_form

  • Lagrangian (field theory)
  • Application of Lagrangian mechanics to field theories

    function on a fiber bundle, wherein the Euler–Lagrange equations can be interpreted as specifying the geodesics on the fiber bundle, leading to topics

    Lagrangian (field theory)

    Lagrangian_(field_theory)

  • Cartan connection
  • Generalization of affine connections

    concept of a principal connection, in which the geometry of the principal bundle is tied to the geometry of the base manifold using a solder form. Cartan

    Cartan connection

    Cartan_connection

  • Geometric quantization
  • Recipe for constructing a quantum analog of a classical physical theory

    an attempt is made to associate a quantum-mechanical observable (a self-adjoint operator on a Hilbert space) with a real-valued function on classical phase

    Geometric quantization

    Geometric_quantization

  • Representation up to homotopy
  • Concept in mathematics

    from the direct sum of the two modules g(A) and ν(A) and should be called adjoint representation. Note however that in the more general case where ρ does

    Representation up to homotopy

    Representation_up_to_homotopy

  • Riemannian manifold
  • Smooth manifold with an inner product on each tangent space

    left-invariant Riemannian metric can be computed explicitly in terms of ge, the adjoint representation of G, and the Lie algebra associated to G. These formulas

    Riemannian manifold

    Riemannian manifold

    Riemannian_manifold

  • Proj construction
  • Projective analogue of the spectrum of a ring

    This situation is to be contrasted with the fact that the Spec functor is adjoint to the global sections functor in the category of locally ringed spaces

    Proj construction

    Proj_construction

AI & ChatGPT searchs for online references containing ADJOINT BUNDLE

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  • Packard
  • Surname or Lastname

    English

    Packard

    English : from Middle English pa(c)k ‘pack’, ‘bundle’ + the Anglo-Norman French pejorative suffix -ard, hence a derogatory occupational name for a peddler.English : pejorative derivative of the Middle English personal name Pack.English : from a Norman personal name, Pachard, Baghard, composed of the Germanic elements pac, bag ‘fight’ + hard ‘hardy’, ‘brave’, ‘strong’.Probably an Americanized spelling of German Packert, Päckert, from Germanic personal names formed with a word meaning ‘battle’ or ‘to fight’; or a variant of Packer 2 (with excrescent -t).

    Packard

  • Areeb
  • Boy/Male

    Arabic, Australian, Muslim, Sindhi

    Areeb

    Skillful; Adroit

    Areeb

  • ÉADAOIN
  • Female

    Irish

    ÉADAOIN

    Variant spelling of Irish Éadan, ÉADAOIN means "face" or perhaps "against" or "opposite."

    ÉADAOIN

  • Dicker
  • Surname or Lastname

    English (southwest)

    Dicker

    English (southwest) : occupational name for a digger of ditches or a builder of dikes, or a topographic name for someone who lived by a ditch or dike, from an agent derivative of Middle English diche, dike (see Dyke).English : regional name from an area of East Sussex, near Hellingly, called ‘the Dicker’ (hence also the hamlets of Upper and Lower Dicker), from Middle English dyker unit of ten (Latin decuria, from decem ‘ten’); the reason for the place being so named is not clear. It has been suggested that the reference is to a bundle of iron rods, in which sense dicras appears in Domesday Book. Such a bundle could have been the rent for property in this iron-working area. Surname forms such as atte dicker occur in the surrounding region in the 13th and 14th centuries.German and Jewish (Ashkenazic) : variant of Dick 2, from an inflected form.North German : variant of Low German Dieker, a topographic or an occupational name for someone who lived or worked at a dike (see Dieck).Americanized spelling of French Decaire.

    Dicker

  • Dextra
  • Girl/Female

    British, English, Latin

    Dextra

    Dyer; Skillful; Dexterous; Adroit; Right-handed

    Dextra

  • COWAL
  • Male

    English

    COWAL

    Anglicized form of Irish Gaelic Comhghall, COWAL means "joint pledge."

    COWAL

  • Balon
  • Surname or Lastname

    English

    Balon

    English : from Old French balon ‘bundle’, ‘roll’, ‘pack’, hence a nickname for a small, rotund man or possibly a metonymic occupational name for a carrier of goods and merchandise.French (Bâlon) : generally regarded as a habitational name from Baalons in the Ardennes, it may however simply be from balon ‘ball’, ‘roll’ (see 1) or a derivative of Bal.

    Balon

  • Dextra
  • Girl/Female

    Latin

    Dextra

    Adroit; skillful.

    Dextra

  • Areeb
  • Boy/Male

    Muslim/Islamic

    Areeb

    Skillful Adroit

    Areeb

  • Joynt
  • Surname or Lastname

    English

    Joynt

    English : presumably from Old French joint ‘united’, ‘joined’. The application as a surname is unclear.

    Joynt

  • Peyvand
  • Girl/Female

    Arabic, Muslim

    Peyvand

    Connection; Joint

    Peyvand

  • COMGAL
  • Male

    Irish

    COMGAL

    Contracted form of Irish Gaelic Comhghall, COMGAL means "joint pledge."

    COMGAL

  • Lav
  • Girl/Female

    Indian, Telugu

    Lav

    Love; To Joint

    Lav

  • Areeb | آریب
  • Boy/Male

    Muslim

    Areeb | آریب

    Skillful, Adroit (1)

    Areeb | آریب

  • Lashah
  • Girl/Female

    Biblical

    Lashah

    To call, to anoint.

    Lashah

  • TAKUMI
  • Male

    Japanese

    TAKUMI

    (1-巧, 2-匠, 3-工) Japanese name TAKUMI means 1) "adroit," 2) "artisan," or 3) "skilful."

    TAKUMI

  • Sheaff
  • Surname or Lastname

    English (Kent)

    Sheaff

    English (Kent) : from Middle English shefe ‘sheaf’, ‘bundle’ (Old English scēaf), hence possibly a metonymic occupational name for a harvest worker, or for someone who paid or collected tithes, from the same term in the sense ‘tenth’ (or other proportion of produce paid as a tithe).Jacob Sheafe (d. 1658) was one of the founds of Boston MA. He is buried in the King’s Chapel Burying Ground there.

    Sheaff

  • Lashah
  • Biblical

    Lashah

    to call; to anoint

    Lashah

  • Truss
  • Surname or Lastname

    English

    Truss

    English : occupational nickname for a peddler, from Old French trousse ‘bundle’, ‘pack’.Ukrainian : nickname from trus ‘rabbit’, typically applied to someone thought to be a coward.

    Truss

  • Fuge
  • Surname or Lastname

    English

    Fuge

    English : from a pet form of Fulcher.German (also Füge) : nickname for a skillful, adroit person, from Middle High German vüege ‘skillful’, ‘fitting’ (see Fiegel).

    Fuge

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Online names & meanings

  • Neelam
  • Boy/Male

    Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Punjabi, Sikh

    Neelam

    Emerald

  • Deonne
  • Girl/Female

    English

    Deonne

    Divine.

  • Thakshak
  • Boy/Male

    Hindu, Indian

    Thakshak

    King Cobra

  • Jambavathy
  • Girl/Female

    Hindu

    Jambavathy

    Daughter of jambavan

  • Arianne
  • Girl/Female

    American, Australian, Chinese, Dutch, Finnish, French, German, Greek, Latin, Swedish

    Arianne

    The Holy One; Black Beauty; Dark One; Very Holy Woman; Similar to Ariadne; Utterly Pure

  • Parnabha | பர்நாபா 
  • Boy/Male

    Tamil

    Parnabha | பர்நாபா 

  • Inkit | இந்கித
  • Boy/Male

    Tamil

    Inkit | இந்கித

    To keep in mind. to point at something

  • Selah
  • Girl/Female

    Biblical

    Selah

    The end, a pause.

  • ILEEN
  • Female

    English

    ILEEN

    Variant spelling of English Eileen, ILEEN means "beauty, radiance." 

  • Dhaivat | தைவத
  • Girl/Female

    Tamil

    Dhaivat | தைவத

    th place in the Raga scale- sa re ga ma pa dha

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Other words and meanings similar to

ADJOINT BUNDLE

AI search in online dictionary sources & meanings containing ADJOINT BUNDLE

ADJOINT BUNDLE

  • Adjoin
  • v. i.

    To lie or be next, or in contact; to be contiguous; as, the houses adjoin.

  • Joint
  • v. t.

    To provide with a joint or joints; to articulate.

  • Joint
  • a.

    Joined; united; combined; concerted; as joint action.

  • Joint
  • a.

    United, joined, or sharing with another or with others; not solitary in interest or action; holding in common with an associate, or with associates; acting together; as, joint heir; joint creditor; joint debtor, etc.

  • Joint
  • n.

    A joining of two things or parts so as to admit of motion; an articulation, whether movable or not; a hinge; as, the knee joint; a node or joint of a stem; a ball and socket joint. See Articulation.

  • Joint
  • a.

    Shared by, or affecting two or more; held in common; as, joint property; a joint bond.

  • Rejoint
  • v. t.

    To reunite the joints of; to joint anew.

  • Adroit
  • a.

    Dexterous in the use of the hands or in the exercise of the mental faculties; exhibiting skill and readiness in avoiding danger or escaping difficulty; ready in invention or execution; -- applied to persons and to acts; as, an adroit mechanic, an adroit reply.

  • Joint
  • v. t.

    To separate the joints; of; to divide at the joint or joints; to disjoint; to cut up into joints, as meat.

  • Joint
  • n.

    The part or space included between two joints, knots, nodes, or articulations; as, a joint of cane or of a grass stem; a joint of the leg.

  • Adjoined
  • imp. & p. p.

    of Adjoin

  • Adjoining
  • p. pr. & vb. n.

    of Adjoin

  • Joint
  • n.

    The space between the adjacent surfaces of two bodies joined and held together, as by means of cement, mortar, etc.; as, a thin joint.

  • Adjoint
  • n.

    An adjunct; a helper.

  • Adjoin
  • v. i.

    To join one's self.

  • Joint
  • v. i.

    To fit as if by joints; to coalesce as joints do; as, the stones joint, neatly.

  • Joint
  • n.

    The place or part where two things or parts are joined or united; the union of two or more smooth or even surfaces admitting of a close-fitting or junction; junction as, a joint between two pieces of timber; a joint in a pipe.

  • Joint
  • v. t.

    To unite by a joint or joints; to fit together; to prepare so as to fit together; as, to joint boards.

  • Adjoin
  • v. t.

    To join or unite to; to lie contiguous to; to be in contact with; to attach; to append.