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Linear representation of a group on the tangent space to a fixed point of the group
In differential geometry, the isotropy representation is a natural linear representation of a Lie group, that is acting on a manifold, on the tangent space
Isotropy_representation
Uniformity in all orientations
Isotropy group An isotropy group is the group of isomorphisms from any object to itself in a groupoid.[dubious – discuss] An isotropy representation is
Isotropy
Mathematical term
{\displaystyle {\mathfrak {g}}} . Succinctly, an adjoint representation is an isotropy representation associated to the conjugation action of G around the
Adjoint_representation
(pseudo-)Riemannian manifold whose geodesics are reversible
irreducible symmetric space G / K is quaternion-Kähler if and only if isotropy representation of K contains an Sp(1) summand acting like the unit quaternions
Symmetric_space
Mathematical concept in differential geometry
follows from his classification that such a representation has the same orbits as the isotropy representation of a symmetric space. Berndt, J; Olmos, C;
Polar_action
Representation of a quantum mechanical system
number of modulus 1, this gives the U(1) factor of the isotropy group. The other part of the isotropy group is parametrized by the unitary matrices on the
Bloch_sphere
Geological concept
properties that are symmetric about an axis that is normal to a plane of isotropy. This transverse plane has infinite planes of symmetry and thus, within
Transverse_isotropy
M_{G}} . Hamiltonian group action Equivariant differential form Isotropy representation Palais, Richard S. (1957). "A global formulation of the Lie theory
Lie_group_action
Solid material whose physical properties are independent of orientation
the finite sizes of atoms and bonding considerations ensure that true isotropy of atomic position will not exist in the solid state, it is possible for
Isotropic_solid
Transformations induced by a mathematical group
in X, the stabilizer subgroup of G with respect to x (also called the isotropy group or little group) is the set of all elements in G that fix x: G x
Group_action
Feature of a system that is preserved under some transformation
(homogeneity) linear momentum p rotation in space (isotropy) angular momentum L = r × p Lorentz-boost (isotropy) boost 3-vector N = tp − Er Discrete symmetry
Symmetry_(physics)
{\displaystyle X} . Assume furthermore that the weights of the isotropy representation of U ( 1 ) {\displaystyle U(1)} on the normal bundle N X Z {\displaystyle
Symplectic_cut
Any of certain special normal subgroups of a group
the isotropy subgroup of any point acts as the identity on its entire orbit. Thus, in case the action is transitive, the normal core of any isotropy subgroup
Core_(group_theory)
anisotropy, both of them are called transverse isotropy (it is called transverse isotropy because there is isotropy in either the horizontal or vertical plane)
Seismic_anisotropy
Non-commutative group with 6 elements
every x in X, we define the stabilizer subgroup of x (also called the isotropy group or little group) as the set of all elements in G that fix x: G x
Dihedral_group_of_order_6
groups appearing, the lists present the Lie algebra of the isotropy group rather than the isotropy group itself. Here Λ3 0C6 ≅ C14 denotes the space of 3-forms
Prehomogeneous_vector_space
Cylindrical conformal map projection
The Mercator projection is conformal. One implication of that is the "isotropy of scale factors", which means that the point scale factor is independent
Mercator_projection
Infinitesimal version of Lie groupoid
{\displaystyle {\mathfrak {g}}_{x}(A)=\ker(\rho _{x})} is a Lie algebra, called the isotropy Lie algebra at x {\displaystyle x} the kernel g ( A ) = ker ( ρ ) {\displaystyle
Lie_algebroid
Internal groupoid in the category of smooth manifolds
. Of course, any fibre E x {\displaystyle E_{x}} becomes a representation of the isotropy group G x {\displaystyle G_{x}} . More generally, representations
Lie_groupoid
Upper-half plane model of hyperbolic non-Euclidean geometry
∈ H , {\displaystyle z\in \mathbb {H} ,} then g = e. The stabilizer or isotropy subgroup of an element z ∈ H {\displaystyle z\in \mathbb {H} } is the set
Poincaré_half-plane_model
Ring that encodes the possible group actions of a finite group
xi in Xi creates an isomorphism G/Gi → Xi, where Gi is the stabilizer (isotropy) subgroup of G at xi. A different choice of representative yi in Xi gives
Burnside_ring
Matrix representing a Euclidean rotation
a requirement of every truly fundamental law (due to the assumption of isotropy of space), and where the same symmetry, when present, is a simplifying
Rotation_matrix
Relation between Lie algebras depicted as a square
algebras. The last row and column here are the orthogonal algebra part of the isotropy algebra in the symmetric decomposition of the exceptional Lie algebras
Freudenthal_magic_square
Family of linear transformations
observers in different inertial frames, as is shown using homogeneity and isotropy of space. The transformation sought after thus must possess the property
Lorentz_transformation
Mathematical group
an isomorphism of k v {\displaystyle k_{v}} -algebras. If we take the isotropy subgroup of G {\displaystyle G} for the valuation class w {\displaystyle
Galois_group
Lie group of Lorentz transformations
that leave a single point (event) fixed. Thus, the Lorentz group is the isotropy subgroup with respect to a point of the isometry group of Minkowski spacetime
Lorentz_group
Physical field surrounding an electric charge
proportional. Materials can have varying extents of linearity, homogeneity and isotropy. The invariance of the form of Maxwell's equations under Lorentz transformation
Electric_field
Ratio of distance on a map to the corresponding distance on the ground
Conversely isotropic scale factors across the map imply a conformal projection. Isotropy of scale implies that small elements are stretched equally in all directions
Scale_(map)
Concept that simultaneity depends on choice of reference frame
alone. In particular, the validity of Einstein synchronisation depends on isotropy of space, homogeneity of time, finite and invariant signal speed. Synchronization
Relativity_of_simultaneity
Category where every morphism is invertible; generalization of a group
which is just the isotropy subgroup at x {\displaystyle x} for the given action (which is why vertex groups are also called isotropy groups). Similarly
Groupoid
Manifold with inversion symmetry
on h {\displaystyle {\mathfrak {h}}} , invariant under the adjoint representation and σ, induces a Riemannian structure on H / K, with H acting by isometries
Hermitian_symmetric_space
Statistical model
defined through the covariance function are the process' stationarity, isotropy, smoothness and periodicity. Stationarity refers to the process' behaviour
Gaussian_process
Non-Euclidean geometry
that space is continuous, homogeneous, isotropic, and without boundaries. Isotropy is guaranteed by the fourth postulate, that all right angles are equal
Elliptic_geometry
the same rate in all directions and that therefore the widely accepted isotropy hypothesis might be wrong. While previous studies already suggested this
Timeline of cosmological theories
Timeline_of_cosmological_theories
Class of spinors constructed using Clifford algebras
known as representation theory, pure spinors (or simple spinors) are spinors that are annihilated, under the Clifford algebra representation, by a maximal
Pure_spinor
Speed of electromagnetic waves in vacuum
the motion of the Earth with respect to this medium, by measuring the isotropy of the speed of light. Beginning in the 1880s several experiments were
Speed_of_light
Function used in signal processing
functions have corners that depend on the choice of the coordinate axes. The isotropy/anisotropy of a two-dimensional window function is shared by its two-dimensional
Window_function
Mathematical structure in differential geometry
authors. The isotropy Lie algebra of a Poisson manifold ( M , π ) {\displaystyle (M,\pi )} at a point x ∈ M {\displaystyle x\in M} is the isotropy Lie algebra
Poisson_manifold
Kumar Samal; Saha, Rajib; Jain, Pankaj; Ralston, John P. (2008). "Testing Isotropy of Cosmic Microwave Background Radiation". Monthly Notices of the Royal
List of unsolved problems in physics
List_of_unsolved_problems_in_physics
Proposed theories of gravity
Thierry (1996). "New test of the Einstein equivalence principle and the isotropy of space". Physical Review D. 52 (6): 3168–3175. arXiv:gr-qc/9504032. Bibcode:1995PhRvD
Alternatives to general relativity
Alternatives_to_general_relativity
Hypothetical vacuum, less stable than true vacuum
Universe Scenario: A Possible Solution Of The Horizon, Flatness, Homogeneity, Isotropy And Primordial Monopole Problems". Phys. Lett. B. 108 (6): 389. Bibcode:1982PhLB
False_vacuum
Time reversal symmetry in physics
entropy? This view, supported by cosmological observations (such as the isotropy of the cosmic microwave background) connects this problem to the question
T-symmetry
Generalization of affine connections
Cartan 1951, pp. 384–385, 477. More precisely, hp is required to be in the isotropy group of φp(p), which is a group in G isomorphic to H. In general, this
Cartan_connection
Quantum mechanical model with coupled spins
The Majumdar–Ghosh model has a gap and falls under the second case. The isotropy of the model is actually not important to the fact that it has an exactly
Majumdar–Ghosh_model
Geometric representation of material yield
«Parametrization of Cauchy Stress Tensor Treated as Autonomous Object Using Isotropy Angle and Skewness Angle» from 2022, https://et.ippt.pan.pl/index
Yield_surface
Mathematical description of spacetime used in relativity
postulate of special relativity, together with homogeneity of spacetime and isotropy of space, it follows that the spacetime interval between two arbitrary
Minkowski_spacetime
Theory of interwoven space and time by Albert Einstein
explicit postulates, but also on several tacit assumptions, including the isotropy and homogeneity of space and the independence of measuring rods and clocks
Special_relativity
{Z} ^{n}} , with determinant equal to ± 1 {\displaystyle \pm 1} . The isotropy subgroup associated to each facet F i {\displaystyle F_{i}} is described
Quasitoric_manifold
Theory of forces and subatomic particles
predominance of matter over antimatter (matter/antimatter asymmetry). The isotropy and homogeneity of the visible universe over large distances seems to require
Standard_Model
Atom of the element hydrogen
dependence on the angular coordinates follows completely generally from this isotropy of the underlying potential: the eigenstates of the Hamiltonian (that is
Hydrogen_atom
Quantum mechanical statistic
peculiar spatial direction associated with the particle that, assuming the isotropy of space, can be identified with the spin of the particle itself". Esposito
Quantum_potential
used for this purpose the principle of relativity, the homogeneity and isotropy of space, and the requirement of reciprocity. Philipp Frank and Hermann
History_of_special_relativity
1988 book by Stephen Hawking
(homogeneity), and that it is identical in every direction that we look, (isotropy). It follows that the universe is non-static. Support was found when two
A_Brief_History_of_Time
Mathematical transformation
method called "minimal projection" by Klein (1893), which was later called "isotropy projection" by Blaschke (1926) emphasizing the relation to oriented circles
Spherical_wave_transformation
Mathematical group
{\displaystyle \ell _{S}(ws)<\ell _{S}(w)} . Sometimes such subgroups are called isotropy groups. Including the entire space V, as the empty intersection. In particular
Parabolic subgroup of a reflection group
Parabolic_subgroup_of_a_reflection_group
Type of transport in differential geometry
symmetry group of M {\displaystyle M} is G = PSL(n+1,R). Let H be the isotropy group of the point [ 1 , 0 , 0 , … , 0 ] {\displaystyle [1,0,0,\ldots
Projective_connection
Non-local formulation of continuum mechanics
{\displaystyle \Omega _{t}} at time t {\displaystyle t} . Applying the isotropy hypothesis, the dependence on vector ξ {\displaystyle {\bf {\xi }}} can
Peridynamics
Group theory theorem
following theorem. If X is a set with transitive group action and the isotropy group or stabilizer of a point x ∈ X is a closed Lie subgroup, then X has
Closed-subgroup_theorem
Mathematical representation of stress in continuum dynamics
"Parametrization of Cauchy Stress Tensor Treated as Autonomous Object Using Isotropy Angle and Skewness Angle". Engineering Transactions. 70 (3): 239–286. doi:10
Stress_space
State of matter
conditions, the diffraction pattern has circular symmetry, expressing the isotropy of the liquid. Radially, the diffraction intensity smoothly oscillates
Liquid
92.1145H. doi:10.1103/PhysRev.92.1145. ISSN 0031-899X. "Anisotropy and Isotropy". Archived from the original on 2012-05-31. Retrieved 2013-12-07. Norris
Acoustoelastic_effect
Outer automorphism group of a free group on n generators
n ) {\displaystyle \mathrm {Out} (F_{n})} is simplicial and has finite isotropy groups. Train track map Automorphism group of a free group Outer space
Out(Fn)
the speed, not on the direction, because the latter would violate the isotropy of space. Now bring in systems K 1 {\displaystyle K_{1}} and K 2 {\displaystyle
Derivations of the Lorentz transformations
Derivations_of_the_Lorentz_transformations
case when the eigenvalues have the same magnitude. Thus a measure of the isotropy around a local region is defined as the following: Q = λ min ( M ) λ max
Harris_affine_region_detector
Statistical theory
{k}})} needs to be inferred. Given a further assumption of statistical isotropy, this spectrum depends only on the length k = | k → | {\displaystyle k=|{\vec
Information_field_theory
Emission of secondary X-rays from a material excited by high-energy X-rays
materials. Glasses most closely approach the ideal of homogeneity and isotropy, and for accurate work, minerals are usually prepared by dissolving them
X-ray_fluorescence
Defunct theory of electromagnetism
follows: Taken together (along with a few other tacit assumptions such as isotropy and homogeneity of space), these two postulates lead uniquely to the mathematics
Lorentz_ether_theory
Japanese philosopher
transformation [点変換]; Statistical mechanics [統計的力学]; Homogeneity [等質性]; Isotropy [等方性]; Intensive quantity [内包量]; First law of thermodynamics [熱力学第一法則];
Hajime_Tanabe
American fluid dynamicist
Within and Above a Mature Corn Canopy-Part A: Statistics and Small Scale Isotropy, Journal of the Atmospheric Sciences 64(8) (2007) 2805–2824. O. Uzol, D
Joseph_Katz_(professor)
Lie algebra classification
curvature. Assuming only space homogeneity with no additional symmetry such as isotropy leaves considerably more freedom in choosing the metric. The following
Bianchi_classification
ISOTROPY REPRESENTATION
ISOTROPY REPRESENTATION
ISOTROPY REPRESENTATION
Surname or Lastname
English
English : probably a variant of Kibble.Americanized spelling of German Gibel or Gibbel (see Giebel).
Boy/Male
Arabic, Muslim
Walking Gently
Girl/Female
Gujarati, Hindu, Indian, Telugu
Great
Boy/Male
Latin
Blessed.
Male
Native American
Native American Cree name KAWACATOOSE means "poor man."
Boy/Male
French
Blond ruler.
Boy/Male
Australian, Irish
Surname
Boy/Male
American, Anglo, British, English
From the Taxed Land
Boy/Male
English Israeli
Tall.
Surname or Lastname
English (Derbyshire)
English (Derbyshire) : habitational name from a place in Derbyshire called Greterakes.
ISOTROPY REPRESENTATION
ISOTROPY REPRESENTATION
ISOTROPY REPRESENTATION
ISOTROPY REPRESENTATION
ISOTROPY REPRESENTATION
n.
The pictorial representation of a scene; a sketch, /ither drawn or painted; as, a fine view of Lake George.
n.
In dramatic composition, one of the principles by which a uniform tenor of story and propriety of representation are preserved; conformity in a composition to these; in oratory, discourse, etc., the due subordination and reference of every part to the development of the leading idea or the eastablishment of the main proposition.
a.
Exhibiting differences of quality or property in different directions; not isotropic.
n.
A description or statement; as, the representation of an historian, of a witness, or an advocate.
n.
A general form or structure common to a number of individuals; hence, the ideal representation of a species, genus, or other group, combining the essential characteristics; an animal or plant possessing or exemplifying the essential characteristics of a species, genus, or other group. Also, a group or division of animals having a certain typical or characteristic structure of body maintained within the group.
n.
A likeness, a picture, or a model; as, a representation of the human face, or figure, and the like.
a.
Isotropic.
n.
A figure or representation of something to come; a token; a sign; a symbol; -- correlative to antitype.
n.
Uniformity of physical properties in all directions in a body; absence of all kinds of polarity; specifically, equal elasticity in all directions.
n.
A dramatic performance; as, a theatrical representation; a representation of Hamlet.
n.
A representation of the world.
n.
The act or art of expressing by means of types or symbols; emblematical or hieroglyphic representation.
n.
Isotropy.
a.
Not isotropic; having different properties in different directions; thus, crystals of the isometric system are optically isotropic, but all other crystals are anisotropic.
a.
Implying representation; representative.
n.
The body of those who act as representatives of a community or society; as, the representation of a State in Congress.
n.
A vessel similar to that described in the first definition above, or the representation of one in a solid block of stone, or the like, used for an ornament, as on a terrace or in a garden. See Illust. of Niche.
n.
A portrait or representation of the face of our Savior on the alleged handkerchief of Saint Veronica, preserved at Rome; hence, a representation of this portrait, or any similar representation of the face of the Savior. Formerly called also Vernacle, and Vernicle.
n.
A radioactive isotope of strontium produced by certain nuclear reactions, and constituting one of the prominent harmful components of radioactive fallout from nuclear explosions; also called radiostrontium. It has a half-life of 28 years.
a.
Having the same properties in all directions; specifically, equally elastic in all directions.