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

Title:

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

Creator:

Misiak, Aleksander and Stasiak, Eugeniusz

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:cfc9db8f-5b95-4e5c-9c57-e20f2b6d9a8b
uuid:cfc9db8f-5b95-4e5c-9c57-e20f2b6d9a8b
doi:10.21136/MB.2008.140618

Subject:

G-space, equivariant map, and pseudo-Euclidean geometry

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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 R0. Thus we have four G-spaces of ϕ-scalars (R, G, hϕ) 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∗q1, A∗q2, . . . , A∗qm) = ϕ(A)·F(q1, q2, . . . , qm) for given independent points q1, q2, . . . , qm ∈ 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 F : (S n−2 ) m → R.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

289-298

Source:

Mathematica bohemica | 2008 Volume:133 | Number:3

Harvested from:

CDK

Metadata only:

false