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Title: Equivariant mappings from vector product into $ G$-spaces of $\varphi $-scalars with $G=O\left( n,1,\mathbb{R}\right) $  (English)
Author: Glanc, Barbara
Author: Misiak, Aleksander
Author: Szmuksta-Zawadzka, Maria
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
Volume: 132
Issue: 3
Year: 2007
Pages: 325-332
Summary lang: English
Category: math
Summary: 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 $m\le n$ linearly independent contravariant vectors of two so far missing types. The problem is resolved by finding the general solution of the functional equation $F( A\underset{1}{\rightarrow }{u},A \underset{2}{\rightarrow }{u},\dots ,A\underset{m}{\rightarrow }{u}) = \varphi \left( A\right) \cdot F( \underset{1}{\rightarrow }{u},\underset{2}{\rightarrow }{u},\dots ,\underset{m}{\rightarrow }{u})$ using two homomorphisms $\varphi $ from a group $G$ into the group of real numbers $\mathbb{R}_{0}=\left( \mathbb{R}\setminus \left\rbrace 0\right\lbrace ,\cdot \right)$.
Keyword: $G$-space
Keyword: equivariant map
Keyword: pseudo-Euclidean geometry
MSC: 53A55
idZBL: Zbl 1174.53007
idMR: MR2355661
Date available: 2009-09-24T22:32:10Z
Last updated: 2012-06-18
Stable URL:
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