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In physics, a non-invertible symmetry is a symmetry of a quantum field theory that is not described by a group, and which in particular does not have
Non-invertible_symmetry
Low energy theories not compatible with string theory
the fusion of the symmetry operators has an element without an inverse, the corresponding symmetry is called a non-invertible symmetry. The above definitions
Swampland_(physics)
Feature of a system that is preserved under some transformation
symmetries, higher group symmetries, non-invertible symmetries, and subsystem symmetries. The transformations describing physical symmetries typically form a
Symmetry_(physics)
Group of transformations under which the object is invariant
with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which
Symmetry_group
The invertibility of a knot is a knot invariant. An invertible link is the link equivalent of an invertible knot. There are only five knot symmetry types
Invertible_knot
Violation of charge-parity symmetry in particle physics and cosmology
CP-symmetry (or charge conjugation parity symmetry): the combination of C-symmetry (charge conjugation symmetry) and P-symmetry (parity symmetry). CP-symmetry
CP_violation
Simplest non-trivial closed knot with three crossings
trefoils are not ambient isotopic.) Though chiral, the trefoil knot is also invertible, meaning that there is no distinction between a counterclockwise-oriented
Trefoil_knot
Isomorphism of an object to itself
isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving
Automorphism
Group that is also a differentiable manifold with group operations that are smooth
concept of continuous symmetry, a celebrated example of which is the circle group. Rotating a circle is an example of a continuous symmetry. For any rotation
Lie_group
Group of 𝑛 × 𝑛 invertible matrices
n} invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices
General_linear_group
Asymmetry of classical and quantum action
class invertible topological field theory, in order to match their higher anomalies on the 4 dimensional boundary. Anomalies in gauge symmetries lead to
Anomaly_(physics)
Branch of mathematics that studies the properties of groups
given by matrix groups, or linear groups. Here, G is a set consisting of invertible matrices of given order n over a field K that is closed under the products
Group_theory
Algebra where x(xy)=(xx)y and (yx)x=y(xx)
{\displaystyle x} and y {\displaystyle y} are invertible then x y {\displaystyle xy} is also invertible with inverse ( x y ) − 1 = y − 1 x − 1 {\displaystyle
Alternative_algebra
Mathematical concept
multivariable function f : Rn → Rn is invertible in a neighborhood of a point p as long as the Jacobian matrix of f at p is invertible. In this case, the Jacobian
Inverse_function
German-born sculptor, inventor, and mathematician (1898–1979)
and discovered the inversions of the platonic solids, including the "invertible cube", which is often sold as an eponymous puzzle, the Schatz cube. From
Paul_Schatz
Open convex self-dual cones
self-dual cones in Euclidean space which have a transitive group of symmetries, i.e. invertible operators that take the cone onto itself. By the Koecher–Vinberg
Symmetric_cone
Algebraic theory
topological order due to the existence of invertible topological phases, which are non-trivial yet host no anyons. Invertible phases are characterized not by their
Algebraic theory of topological quantum information
Algebraic_theory_of_topological_quantum_information
Interdisciplinary field studying perception, cognition, and characteristics of art
and explicit aesthetic preferences of symmetry in abstract patterns found the difference between art experts and non-experts only arose in the explicit rating
Psychology_of_art
Matrix with one nonzero entry in each row and column
{2}}\end{bmatrix}}.} An invertible matrix A is a generalized permutation matrix if and only if it can be written as a product of an invertible diagonal matrix
Generalized permutation matrix
Generalized_permutation_matrix
Introductory article
gauge symmetry holds, and energy is conserved, then charge must be conserved. As discussed above, the gauge transformations for classical (i.e., non-quantum
Introduction_to_gauge_theory
Group of flat spacetime symmetries
non-abelian Lie group of three-dimensional rotations (J); boosts, transformations connecting two uniformly moving bodies (K). The last two symmetries
Poincaré_group
Set with associative invertible operation
naturally in the study of symmetries and geometric transformations: the symmetries of an object form a group, called the symmetry group of the object, and
Group_(mathematics)
Uniform star polyhedron with 112 faces
are not quite regular. Unlike most snub polyhedra, it has reflection symmetries. George Olshevsky nicknamed it the yog-sothoth (after the Cthulhu Mythos
Small retrosnub icosicosidodecahedron
Small_retrosnub_icosicosidodecahedron
Classification of crystalline materials by their three-dimensional structural geometry
crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point). A lattice system is a set of Bravais lattices
Crystal_system
Type of order at absolute zero
to the discrete symmetry of the crystal. Similarly this holds for rotational symmetry. Such a change in symmetry is called symmetry breaking. The essence
Topological_order
Imbalance of matter and antimatter in the observable universe
dipole moments in equilibrium states requires violation of T-symmetry. That way finding a non zero electric dipole moment would imply the existence of T-violating
Baryon_asymmetry
Plane curve: conic section
y=ax^{2}+bx+c} (with a ≠ 0 {\displaystyle a\neq 0} ) is a parabola with its axis of symmetry coincident with the y-axis. Conversely, every such parabola is the graph
Parabola
Relations between quark-gluon families in particle physics
In particle physics, the family symmetries or horizontal symmetries are various discrete, global, or local symmetries between different quark-lepton families
Family_symmetries
In physics and geometry: conjectured relation between pairs of Calabi–Yau manifolds
In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau manifolds. The term refers
Mirror symmetry (string theory)
Mirror_symmetry_(string_theory)
Set of rules pertaining to pericyclic reactions
occurrence, and such reactions are called symmetry-forbidden. Their opposites are symmetry-allowed. Although the symmetry-imposed barrier is often formidable
Woodward–Hoffmann_rules
Solid with 2 parallel n-gonal bases connected by n parallelograms
} The symmetry group of a right n-sided prism with regular base is Dnh of order 4n, except in the case of a cube, which has the larger symmetry group
Prism_(geometry)
Class of molecular symmetry
Molecular symmetry in physics and chemistry describes the symmetry present in molecules and the classification of molecules according to their symmetry. Molecular
Symmetry of diatomic molecules
Symmetry_of_diatomic_molecules
Catalan solid with 12 faces
cuboctahedron; they share the same symmetry, the octahedral symmetry. It is face-transitive, meaning the symmetry group of the solid acts transitively
Rhombic_dodecahedron
Regular object in four dimensional geometry
The vertices of the 24-cell form the group of units (i.e. the group of invertible elements) in the Hurwitz quaternion ring (this group is also known as
24-cell
congruent, and the polyhedron has a high degree of reflectional and rotational symmetry. Uniform polyhedra can be divided between convex forms with convex regular
List_of_uniform_polyhedra
Natural number
been underlined, both in handwriting and on printed labels. The sixfold symmetry of snowflakes arises from the hexagonal crystal structure of ordinary ice
6
Fibration symmetry is a mathematical notion of symmetry in networks that overcomes the limitations of classical group-theoretic symmetry through automorphisms
Fibration_symmetry
Construction in group theory
the general linear group, which is generally defined axiomatically as "invertible functions preserving the linear (vector space) structure", the projective
Projective_linear_group
Two geometries based on axioms closely related to those specifying Euclidean geometry
Karamazov, Dostoevsky discusses non-Euclidean geometry through his character Ivan. Christopher Priest's novel Inverted World describes the struggle of
Non-Euclidean_geometry
Symmetry group of a configuration in space
space group is the symmetry group of a repeating pattern in space, usually in three dimensions. The elements of a space group (its symmetry operations) are
Space_group
Pictorial representation of the behavior of subatomic particles
}A^{\nu }\right)\,.} The quadratic form defining the propagator is non-invertible. The reason is the gauge invariance of the field; adding a gradient
Feynman_diagram
Four-dimensional analogue of the cube
Its symmetry is 4[4]2, order 32. It also has a lower symmetry construction, , or 4{}×4{}, with symmetry 4[2]4, order 16. This is the symmetry if the
Tesseract
Matrix equal to its transpose
matrix A {\displaystyle A} is said to be symmetrizable if there exist an invertible diagonal matrix D {\displaystyle D} and symmetric matrix S {\displaystyle
Symmetric_matrix
Application of a function to each point in a data set
can transform to any distribution with an invertible cumulative distribution function. If G is an invertible cumulative distribution function, and U is
Data transformation (statistics)
Data_transformation_(statistics)
Group representation
into the group of invertible operators on the vector space. Representations play an important role in the study of continuous symmetry. A great deal is
Representation_of_a_Lie_group
Group of isotopy classes of a topological automorphism group
of X that preserves A, i.e. f: X → X is invertible and f(A) = A. If K ⊂ S3 is a knot or a link, the symmetry group of the knot (resp. link) is defined
Mapping_class_group
Mathematical group that can be generated as the set of powers of a single element
numbers), that is generated by a single element. That is, it is a set of invertible elements with a single associative binary operation, and it contains an
Cyclic_group
Groups of point isometries in 3 dimensions
as one of them. The symmetry group of an object is sometimes also called its full symmetry group, as opposed to its proper symmetry group, the intersection
Point groups in three dimensions
Point_groups_in_three_dimensions
Five-pointed star polygon
with a pentagram constructed inside it, the regular pentagram has as its symmetry group the dihedral group of order 10. It can be seen as a net of a pentagonal
Pentagram
Vector used in astronomy
quantities generally correspond to a symmetry of the system. The conservation of the LRL vector corresponds to an unusual symmetry; the Kepler problem is mathematically
Laplace–Runge–Lenz_vector
Form of a matrix
{\textstyle A} is a real skew-symmetric matrix, then I + A {\textstyle I+A} is invertible, where I {\textstyle I} is the identity matrix. If A {\textstyle A} is
Skew-symmetric_matrix
Molecular orbital theory applied to transition metal complexes
their σ-symmetry orbitals form bonding and anti-bonding combinations with the dz2 and dx2−y2 orbitals. The dxy, dxz and dyz orbitals remain non-bonding
Ligand_field_theory
Proposed state of matter in semiconductors
state does not break charge conservation symmetry and spin- S z {\displaystyle S_{z}} conservation symmetry (in order to have well defined Hall conductances)
Quantum_spin_Hall_effect
Symmetrical calligraphic or typographic visual pun
observation. Most ambigrams are visual palindromes that rely on some kind of symmetry, and they can often be interpreted as visual puns. Although the concept
Ambigram
Uniformity in all orientations
Bi isotropic Symmetry A groupoid G {\displaystyle {\mathcal {G}}} is a category where all morphisms are isomorphisms, i.e., invertible. If G ∈ G {\displaystyle
Isotropy
Nonassociative algebra over the real numbers
numbers. Unlike the standard octonions, they contain non-zero elements which are non-invertible. Also the signatures of their quadratic forms differ:
Split-octonion
Notation in physics and chemistry
heteronuclear diatomic molecules, the u/g symbol does not correspond to any exact symmetry of the electronic molecular Hamiltonian. In the case of less symmetric
Molecular_term_symbol
the frequency spectrum. (These transforms are generally designed to be invertible.) In the case of the Fourier transform, each basis function corresponds
List of Fourier-related transforms
List_of_Fourier-related_transforms
Subclass of matrices
sense.) Any strictly diagonally dominant complex square matrix is non-singular (invertible). This is also known as Lévy-Desplanques theorem, whose practical
Diagonally_dominant_matrix
Group of symmetries of an n-dimensional hypercube
and may be represented as the set of invertible matrices with entries only 0, 1, or −1 and with exactly one non-zero entry in each row or column. The
Hyperoctahedral_group
Polyhedron resulting from the snub operation
reflection symmetry and hence sometimes have two enantiomorphous (left- and right-handed) forms which are reflections of each other. Their symmetry groups
Snub_polyhedron
Automorphism group of the Klein quartic
isomorphic to PSL(2, 5). The general linear group GL(2, 7) consists of all invertible 2×2 matrices over F7, the finite field with 7 elements. These have nonzero
PSL(2,7)
Group homomorphism into the general linear group over a vector space
automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication
Group_representation
Natural number
(Number of nonsquare simple perfect squared rectangles of order n up to symmetry)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. DHAMIJA
9
Electronic circuit with two signal transmission lines of matching impedance
directions on the line. Balance and symmetry are usually associated with reflected horizontal and vertical physical symmetry respectively as shown in figures
Balanced_circuit
Russian-American physicist (born 1963)
2+1-dimensional invertible phase, and his ideas have been used in generalized-cohomology classifications of symmetry-protected topological phases with symmetry group
Alexei_Kitaev
Concept in mathematics
&e'_{n}\end{bmatrix}}={\begin{bmatrix}e_{1}&\cdots &e_{n}\end{bmatrix}}S} with S an invertible n×n matrix. Now the new matrix representation for the symmetric bilinear
Symmetric_bilinear_form
Function that is invariant under all permutations of its variables
subtracting the sum over odd permutations. These operations are of course not invertible, and could well result in a function that is identically zero for nontrivial
Symmetric_function
Type of group in mathematics
non-degenerate symmetric bilinear form or quadratic form on a vector space over a field, the orthogonal group of the form is the group of invertible linear
Orthogonal_group
also applies to non-invertible elements y. If A is finite-dimensional over R or C, invertible elements a in A are dense, since invertibility is equivalent
Mutation_(Jordan_algebra)
Sporadic simple group
Previously, R. A. Wilson had found explicitly (with the aid of a computer) two invertible 196,882 by 196,882 matrices (with elements in the field of order 2) which
Monster_group
Array of numbers
is invertible if and only if its determinant is invertible in R, generalizing the situation over a field F, where every nonzero element is invertible. Matrices
Matrix_(mathematics)
Unique knot with a crossing number of four
q − 1 + q − 2 . {\displaystyle V(q)=q^{2}-q+1-q^{-1}+q^{-2}.\ } The symmetry between q {\displaystyle q} and q − 1 {\displaystyle q^{-1}} in the Jones
Figure-eight knot (mathematics)
Figure-eight_knot_(mathematics)
Technology of power electronics
Optimal switching patterns must have quarter-wave and half-wave symmetry, as well as symmetry about 30 degrees and 150 degrees. Switching patterns are never
Power_electronics
Branch of mathematics that studies abstract algebraic structures
representation theory of groups, in which elements of a group are represented by invertible matrices such that the group operation is matrix multiplication. Representation
Representation_theory
Type of pendulum
axis of the arms is negligible. In addition, most arms have rotational symmetry such that the moments of inertia in two of the principal axes are equal
Furuta_pendulum
Mathematical concept
bijective if 2 is invertible in R, with the inverse given by multiplication with 1/2. An ε-quadratic form ψ ∈ Qε(M) is called non-degenerate if the associated
Ε-quadratic_form
Moufang identities hold in any octonion algebra. It follows that the invertible elements in any octonion algebra form a Moufang loop, as do the elements
Octonion_algebra
Natural number
15, 33}. There are 7 frieze groups in two dimensions, consisting of symmetries of the plane whose group of translations is isomorphic to the group of
7
Genus of viruses
Petuvirus are non-enveloped, with icosahedral geometries, and T=7 symmetry. The diameter is around 45-50 nm. Genomes are circular and non-segmented. Its
Petuvirus
Matrix operation which flips a matrix over its diagonal
{A} ^{-1}\right)^{\text{T}}.} The transpose of an invertible matrix is also invertible, and its inverse is the transpose of the inverse of the original
Transpose
Number associated with symmetric convex bodies
B} and B ∘ {\displaystyle B^{\circ }} . If T {\displaystyle T} is an invertible linear transformation, then ( T B ) ∘ = ( T − 1 ) ∗ B ∘ {\displaystyle
Mahler_volume
Marked objects for finding random numbers
it in a strictly controlled way, it is not typically the case and the symmetry of the die is broken when it is thrown, effectively yielding a random number
Dice
Type of electrical device
electrical performance. The advantage of the toroidal shape is that, due to its symmetry, the amount of magnetic flux that escapes outside the core (leakage flux)
Toroidal inductors and transformers
Toroidal_inductors_and_transformers
Chaotic map from the unit square into itself
off the dyadic expansion of x. Unlike the tent map, the baker's map is invertible. The baker's map preserves the two-dimensional Lebesgue measure. The map
Baker's_map
Square matrix which is its own inverse
roots of the identity matrix. This is a consequence of the fact that any invertible matrix multiplied by its inverse is the identity. The 2 × 2 {\displaystyle
Involutory_matrix
Transformations induced by a mathematical group
( n , K ) {\displaystyle \operatorname {GL} (n,K)} , the group of the invertible matrices of dimension n {\displaystyle n} over a field K {\displaystyle
Group_action
Rotating or sliding component that transmits variable motion to a follower
is linear with rotation, such as the scroll plate in a scroll chuck. Non-invertible functions, which require the groove to self-intersect, can be implemented
Cam_(mechanism)
Commutative group (mathematics)
group with respect to its addition operation. In a commutative ring the invertible elements, or units, form an abelian multiplicative group. In particular
Abelian_group
Homomorphisms between simple modules over the same ring are isomorphisms or zero
from M to N that commutes with the action of the group, then either φ is invertible, or φ = 0. An important special case occurs when M = N, i.e. φ is a self-map;
Schur's_lemma
Electronic circuit with two stable states
considered as an active inverting feedback network for the other inverting amplifier. Thus the two stages are connected in a non-inverting loop although the
Flip-flop_(electronics)
Generic flatness Irrelevant ideal Locally ringed space Coherent sheaf Invertible sheaf Sheaf cohomology Coherent sheaf cohomology Hirzebruch–Riemann–Roch
List of algebraic geometry topics
List_of_algebraic_geometry_topics
Matrix defined using smaller matrices called blocks
the Schur complement of D in P: P/D = A − BD−1C must be invertible. If A and D are both invertible, then: [ A B C D ] − 1 = [ ( A − B D − 1 C ) − 1 0 0 (
Block_matrix
Type of supersymmetric quantum field theory
is positive definite, then g i j ¯ {\displaystyle g_{i{\bar {j}}}} is invertible, allowing the inverse metric g i j ¯ {\displaystyle g^{i{\bar {j}}}} to
Wess–Zumino_model
Technology for constructing integrated circuits
transceivers for many types of communication. The principle of complementary symmetry was first introduced by George Sziklai in 1953 who then discussed several
CMOS
Statistic quantifying the association between two events
mathematical invertible property when studying disease survival vs. onset incidence. This phenomenon of OR invertibility vs. RR non-invertibility is best illustrated
Odds_ratio
Type of curve in hyperbolic geometry
open half-plane of the axis inverts to P' whose angle of parallelism is the complement of that of P. This quasi-symmetry generalizes to hyperbolic spaces
Hypercycle_(geometry)
Physical and science fiction concept
1292–1292. doi:10.1126/science.124.3235.1292.a. Villata, M. (April 2011). "CPT symmetry and antimatter gravity in general relativity". EPL (Europhysics Letters)
Anti-gravity
Category where every morphism is invertible; generalization of a group
function replacing the binary operation; Category in which every morphism is invertible. A category of this sort can be viewed as augmented with a unary operation
Groupoid
Integration for Grassmann variables
again mean right derivatives. When the function D {\displaystyle D} is invertible in Λ m ∣ n , {\displaystyle \Lambda ^{m\mid n},} J = ∂ ( x , θ ) ∂ ( y
Berezin_integral
NON INVERTIBLE-SYMMETRY
NON INVERTIBLE-SYMMETRY
Female
Vietnamese
Vietnamese name NGON means "good communication."
Female
Russian
(Ðона) Russian name derived from Greek enatos, NONA means "ninth." Compare with another form of Nona.
Male
English
 Short form of English/Scottish Ronald, RON means "wise ruler." Compare with another form of Ron.
Biblical
same as Non
Girl/Female
Biblical
Posterity, a fish, eternal.
Male
English
 English short form of Spanish Alonso, LON means "noble and ready." Compare with another form of Lon.
Female
English
(רï‹×Ÿ) Hebrew unisex name RON means "joy, song." Compare with strictly masculine Ron.
Male
English
 Pet form of English Jonathan, JON means "God has given." Compare with other forms of Jon.
Female
Hawaiian
Hawaiian name NOE means "mist; misty rain."
Boy/Male
American, Australian
Little Son
Boy/Male
Greek
Son of Apollo.
Male
French
French form of Greek Noe, NOÉ means "rest."
Surname or Lastname
English, German, Dutch, French (Noé, Noë), Spanish (Noé), Catalan (Noè)
English, German, Dutch, French (Noé, Noë), Spanish (Noé), Catalan (Noè) : from the Biblical personal name Noach ‘Noah’, which means ‘comfort’ in Hebrew. According to the Book of Genesis, Noah, having been forewarned by God, built an ark into which he took his family and representatives of every species of animal, and so was saved from the flood that God sent to destroy the world because of human wickedness. The personal name was not common among non-Jews in the Middle Ages, but the Biblical story was an extremely popular subject for miracle plays. In many cases, therefore, the surname probably derives from a nickname referring to someone who had played the part of Noah in a miracle play or pageant, rather than from a personal name.
Male
Hebrew
(רï‹×Ÿ) Hebrew unisex name RON means "joy, song." Compare with another form of Ron.
Male
Norwegian
Danish and Norwegian form of Old Norse Hákon, HÅKON means "high son."
Female
English
Variant spelling of English Noah, NOA means "motion."Â
Biblical
posterity; a fish; eternal
Male
Scandinavian
 Scandinavian form of Icelandic Jóhann, JON means "God is gracious." Compare with other forms of Jon.
Female
English
Short form of English Nancy, NAN means "favor; grace."
Female
English
Variant form of Old English Nona, NONI means "ninth."
NON INVERTIBLE-SYMMETRY
NON INVERTIBLE-SYMMETRY
Boy/Male
Latin
Revered.
Girl/Female
American, Australian, British, English, Irish
Pale-skinned; Dark; Black; Pale; White
Girl/Female
Greek
Highly regarded.
Boy/Male
Arabic, Muslim
Popularity
Girl/Female
Tamil
Lakshetha | லாகà¯à®·à¯‡à®¤à®¾
Distinguished
Girl/Female
Hindu
Three, Triple
Girl/Female
Indian, Sanskrit
Soft
Boy/Male
Indian
Absorber, Attractive
Boy/Male
Arabic, Muslim
Servant of the Descender
Girl/Female
Tamil
Dusky
NON INVERTIBLE-SYMMETRY
NON INVERTIBLE-SYMMETRY
NON INVERTIBLE-SYMMETRY
NON INVERTIBLE-SYMMETRY
NON INVERTIBLE-SYMMETRY
a.
No one; not one; not anything; -- frequently used also partitively, or as a plural, not any.
a.
No; not. See No, a.
a.
Not to be diverted or turned aside.
a.
Not fertile; infertile; barren.
a.
Capable of, or admitting of, reverting or being reverted; as, a revertible estate.
a.
Capable of being inverted or turned.
p. pr. & vb. n.
of Non-pros
a.
Unfruitful; not producing young; barren; infertile.
a.
Not vendible or salable.
a.
Capable of being changed or converted; as, invertible sugar.
n.
Quality of being inventible.
a.
Not pregnant; unfertilized or infertile.
a.
No; not any; -- used adjectively before a vowel, in old style; as, thou shalt have none assurance of thy life.
a.
Incapable of being turned or changed.
a.
Not any; not one; none.
a.
Not fertile; not productive; barren; sterile; as, an infertile soil.