About: Equivariant map

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Equivariant map Goto Sponge NotDistinct Permalink

An Entity of Type : yago:YagoPermanentlyLocatedEntity, within Data Space : dbpedia.org associated with source document(s)
QRcode icon

http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FEquivariant_map

In mathematics, equivariance is a form of symmetry for functions from one space with symmetry to another (such as symmetric spaces). A function is said to be an equivariant map when its domain and codomain are acted on by the same symmetry group, and when the function commutes with the action of the group. That is, applying a symmetry transformation and then computing the function produces the same result as computing the function and then applying the transformation.

Attributes	Values
rdf:type	Thing yago:Abstraction100002137 yago:Act100030358 yago:Event100029378 yago:GroupAction101080366 yago:PsychologicalFeature100023100 yago:WikicatGroupActions yago:YagoPermanentlyLocatedEntity
rdfs:label	Äquivariante Abbildung (de) Equivariant map (en) Équivariance (fr) Aplicação equivariante (pt) 等变映射 (zh)
rdfs:comment	Unter einer äquivarianten Abbildung versteht man in der Mathematik eine Abbildung, die mit der Wirkung einer Gruppe kommutiert. (de) 在数学中，一个等变映射（equivariant map）是两个集合之间与群作用交换的一个函数。具体地，设 G 是一个群，X 与 Y 是两个关联的 G-集合。一个函数 f : X → Y 称为等变，如果 f(g·x) = g·f(x) 对所有 g ∈ G 与 x ∈ X 成立。注意如果其中一个或两个作用是右作用，则等变条件必须适当地修改： f(x·g) = f(x)·g ; （右-右）f(x·g) = g−1·f(x) ; （右-左）f(g·x) = f(x)·g−1 ; （左-右）等变映射是 G-集合范畴（对一个取定的 G）中的同态。从而它们也称为 G-映射或 G-同态。G-集合的同构就是等变双射。等变条件也能理解为下面的交换图表。注意表示映射取元素得到。 (zh) In mathematics, equivariance is a form of symmetry for functions from one space with symmetry to another (such as symmetric spaces). A function is said to be an equivariant map when its domain and codomain are acted on by the same symmetry group, and when the function commutes with the action of the group. That is, applying a symmetry transformation and then computing the function produces the same result as computing the function and then applying the transformation. (en) En mathématiques, l'équivariance est une forme de symétrie de fonctions d'un espace par symétrie avec un autre (tels que les espaces symétriques). Une fonction est appelée application équivariante quand son domaine et son codomaine agissent sur le même groupe de symétrie, et quand la fonction commute avec l'action de groupe. Ainsi, appliquer une transformation de symétrie puis calculer la fonction produit le même résultat que le calcul de la fonction suivi de la transformation. (fr) Em matemática, uma aplicação invariante é uma função entre dois conjuntos que comuta com a ação de um grupo. Especificamente, seja G um grupo e sejam X e Y os G-conjuntos associados. Uma função f : X → Y é dita equivariante se f(g·x) = g·f(x) para todo g ∈ G e todo x em X. Note que se uma ou ambas as ações forem ações à direita a condição que define a equivariância deve ser modificada adequadamente: f(x·g) = f(x)·g ; (direita-direita)f(x·g) = g−1·f(x) ; (direita-esquerda)f(g·x) = f(x)·g−1 ; (esquerda-esquerda) (pt)
rdfs:seeAlso	Representation theory Isomorphisms
foaf:depiction
dcterms:subject	Symmetry Representation theory Group actions (mathematics)
Wikipage page ID	422711 (xsd:integer)
Wikipage revision ID	1041208705 (xsd:integer)
Link from a Wikipage to another Wikipage	Scalar (mathematics) Schur's Lemma Module (mathematics) Monotonic function Homomorphism Curtis–Hedlund–Lyndon theorem Incenter Invariant (mathematics) Commutative property Continuous function Mathematics Mean Median Natural transformation Circumcenter Function (mathematics) Morphism Congruence (geometry) Equivariant cohomology Equivariant stable homotopy theory Equivariant topology Statistical inference Orthocenter Similarity (geometry) Bijective Commutative diagram Functor Functor category Perimeter Subgroup Symmetric space Symmetry Symmetry group Automorphism Category of sets Central tendency Centroid Irreducible representation Linear function (calculus) Linear map Representation theory of finite groups Affine transformation Symmetry Field (mathematics) Isomorphism Group (mathematics) Group action (mathematics) Invariant estimator Isomorphic Triangle center Area Representation theory Triangle Zero map Group actions (mathematics) Group ring Ordinal data Category (mathematics) Category of topological spaces Set (mathematics) Cellular automata Category of vector spaces Up to Robust statistics Topological space Simple module Linear representation Statistical estimation
sameAs	Equivariant map Equivariant map Equivariant map

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 54 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software