Displaying similar documents to “Equivariant maps between certain G -spaces with  G = O ( n - 1 , 1 ) .”

Equivariant mappings from vector product into G -spaces of ϕ -scalars with G = O n , 1 , ℝ

Barbara Glanc, Aleksander Misiak, Maria Szmuksta-Zawadzka (2007)

Mathematica Bohemica

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There are four kinds of scalars in the n -dimensional pseudo-Euclidean geometry of index one. In this note, we determine all scalars as concomitants of a system of m ≤ n linearly independent contravariant vectors of two so far missing types. The problem is resolved by finding the general solution of the functional equation F ( A → 1 u , A → 2 u , ⋯ , A → m u ) = ϕ A · F ( → 1 u , → 2 u , ⋯ , → m u ) using two homomorphisms ϕ from a group G into the group of real numbers ℝ 0 = ℝ ∖ 0 , · .

G -space of isotropic directions and G -spaces of ϕ -scalars with G = O ( n , 1 , ℝ )

Aleksander Misiak, Eugeniusz Stasiak (2008)

Mathematica Bohemica

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There exist exactly four homomorphisms ϕ from the pseudo-orthogonal group of index one G = O ( n , 1 , ℝ ) into the group of real numbers ℝ 0 . Thus we have four G -spaces of ϕ -scalars ( ℝ , G , h ϕ ) in the geometry of the group G . The group G operates also on the sphere S n - 2 forming a G -space of isotropic directions ( S n - 2 , G , * ) . In this note, we have solved the functional equation F ( A * q 1 , A * q 2 , ⋯ , A * q m ) = ϕ ( A ) · F ( q 1 , q 2 , ⋯ , q m ) for given independent points q 1 , q 2 , ⋯ , q m ∈ S n - 2 with 1 ≤ m ≤ n and an arbitrary matrix A ∈ G considering each of all four homomorphisms. Thereby we have determined all equivariant mappings...

Equivariant mappings from vector product into G -space of vectors and ε -vectors with G = O ( n , 1 , ℝ )

Barbara Glanc, Aleksander Misiak, Zofia Stepień (2005)

Mathematica Bohemica

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In this note all vectors and ε -vectors of a system of m ≤ n linearly independent contravariant vectors in the n -dimensional pseudo-Euclidean geometry of index one are determined. The problem is resolved by finding the general solution of the functional equation F ( A → 1 u , A → 2 u , ⋯ , A → m u ) = ( det A ) λ · A · F ( → 1 u , → 2 u , ⋯ , → m u ) with λ = 0 and λ = 1 , for an arbitrary pseudo-orthogonal matrix A of index one and given vectors → 1 u , → 2 u , ⋯ , → m u .

Degree of T-equivariant maps in ℝⁿ

Joanna Janczewska, Marcin Styborski (2007)

Banach Center Publications

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A special case of G-equivariant degree is defined, where G = ℤ₂, and the action is determined by an involution T : ℝ p ⊕ ℝ q → ℝ p ⊕ ℝ q given by T(u,v) = (u,-v). The presented construction is self-contained. It is also shown that two T-equivariant gradient maps f , g : ( ℝ ⁿ , S n - 1 ) → ( ℝ ⁿ , ℝ ⁿ ∖ 0 ) are T-homotopic iff they are gradient T-homotopic. This is an equivariant generalization of the result due to Parusiński.

Positivity and Kleiman transversality in equivariant K -theory of homogeneous spaces

Dave Anderson, Stephen Griffeth, Ezra Miller (2011)

Journal of the European Mathematical Society

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We prove the conjectures of Graham–Kumar [GrKu08] and Griffeth–Ram [GrRa04] concerning the alternation of signs in the structure constants for torus-equivariant K -theory of generalized flag varieties G / P . These results are immediate consequences of an equivariant homological Kleiman transversality principle for the Borel mixing spaces of homogeneous spaces, and their subvarieties, under a natural group action with finitely many orbits. The computation of the coefficients in the expansion...

The equivariant universality and couniversality of the Cantor cube

Michael G. Megrelishvili, Tzvi Scarr (2001)

Fundamenta Mathematicae

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Let ⟨G,X,α⟩ be a G-space, where G is a non-Archimedean (having a local base at the identity consisting of open subgroups) and second countable topological group, and X is a zero-dimensional compact metrizable space. Let ⟨ H ( 0 , 1 ℵ ₀ ) , 0 , 1 ℵ ₀ , τ ⟩ be the natural (evaluation) action of the full group of autohomeomorphisms of the Cantor cube. Then (1) there exists a topological group embedding φ : G ↪ H ( 0 , 1 ℵ ₀ ) ; (2) there exists an embedding ψ : X ↪ 0 , 1 ℵ ₀ , equivariant with respect to φ, such that ψ(X) is an equivariant retract of 0 , 1 ℵ ₀ with respect...