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...
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representations. An equivariant map is often called an intertwining map of representations. Also, in the case of a group G, it is on occasion called a G-map. Isomorphic...
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space V with an invariant quaternionic structure, i.e., an antilinear equivariant map j : V → V {\displaystyle j\colon V\to V} which satisfies j 2 = − 1...
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of the vector bundle, and the projection to Minkowski space is an equivariant map. Therefore, the Poincaré group also acts on the space of sections....
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vector space V with an invariant real structure, i.e., an antilinear equivariant map j : V → V {\displaystyle j\colon V\to V} which satisfies j 2 = + 1...
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equivariant maps from this G {\displaystyle G} -set to itself are in bijection with G {\displaystyle G} . But it is easy to see that (1) these maps form...
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maps f : X → Y {\displaystyle f:X\to Y} , and while equivariant topology also considers such maps, there is the additional constraint that each map "respects...
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In mathematics, equivariant cohomology (or Borel cohomology) is a cohomology theory from algebraic topology which applies to topological spaces with a...
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f ( g x ) = g f ( x ) {\displaystyle f(gx)=gf(x)} ; i.e., f is an equivariant map. We write F G ( X , Y ) = F ( X , Y ) G {\displaystyle F_{G}(X,Y)=F(X...
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operation whose result is insensitive to the order of its arguments Equivariant map, a function whose composition with another function has the commutative...
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with equivariant map P → X {\displaystyle P\to X} ; an arrow from P → T {\displaystyle P\to T} to P ′ → T ′ {\displaystyle P'\to T'} is a bundle map (i...
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Tensor (section As multilinear maps)
{\text{GL}}(W)} ). Then a tensor of type ρ {\displaystyle \rho } is an equivariant map T : F → W {\displaystyle T:F\to W} . Equivariance here means that T...
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smooth, depending on the setting) and the projection map π {\displaystyle \pi } between them is equivariant: π ∘ g = g ∘ π {\displaystyle \pi \circ g=g\circ...
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default. The composition of equivariant maps is again an equivariant map. There is a category of representations with equivariant maps as its morphisms. They...
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In mathematics, a Cannon–Thurston map is any of a number of continuous group-equivariant maps between the boundaries of two hyperbolic metric spaces extending...
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morphisms: equivariant maps composition: the composition of equivariant maps identities: the identity function (which is an equivariant map). The category...
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representation Lie algebra representation Maschke's theorem Schur's lemma Equivariant map Frobenius reciprocity Induced representation Restricted representation...
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Delta operator (redirect from Shift-equivariant)
operator is defined to be a shift-equivariant linear transformation on polynomials in x {\displaystyle x} that maps x {\displaystyle x} to a nonzero constant...
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all g in G and all x in X. Morphisms of G-sets are also called equivariant maps or G-maps. The composition of two morphisms is again a morphism. If a morphism...
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section s {\displaystyle s} of E {\displaystyle E} let the corresponding equivariant map be ψ ( s ) {\displaystyle \psi (s)} . The covariant derivative on E...
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differential geometry, the localization formula states: for an equivariantly closed equivariant differential form α {\displaystyle \alpha } on an orbifold...
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Cartan connection (category Maps of manifolds)
v of the induced vector bundle V over M can be thought of as an H-equivariant map P → V. This is the point of view we shall adopt. Let X be a vector...
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In mathematics, the equivariant algebraic K-theory is an algebraic K-theory associated to the category Coh G ( X ) {\displaystyle \operatorname {Coh}...
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\pi (g)v=v,\,g\in G\}.} If f : V → W {\displaystyle f:V\to W} is an equivariant map between two representations, then its kernel is a subrepresentation...
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:P_{\operatorname {Spin} }\rightarrow P_{\operatorname {SO} }(E)} is an equivariant 2-fold covering map such that π ∘ ϕ = π P {\displaystyle \pi \circ \phi =\pi _{P}\quad...
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In differential geometry, an equivariant differential form on a manifold M acted upon by a Lie group G is a polynomial map α : g → Ω ∗ ( M ) {\displaystyle...
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make the momentum map coadjoint equivariant. However, in general the coadjoint action must be modified to make the map equivariant (this is the case for...
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which is of independent interest: Lemma — Let p:V → W be a surjective equivariant map between representations. If V is semisimple, then p splits; i.e., it...
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and an equivariant map from E × X {\displaystyle E\times X} to X n . {\displaystyle X^{n}.} Pulling back u n {\displaystyle u^{n}} by this map gives an...
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The G {\displaystyle G} -equivariant map from E G {\displaystyle EG} to a single point ∗ {\displaystyle *} induces a natural map η: X G = F ( ∗ , X ) G...
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