Equivariant mappings from vector product into $G$-spaces of $\varphi$-scalars with $G=O\left(n,1,ℝ\right)$

Glanc, Barbara, Misiak, Aleksander, and Szmuksta-Zawadzka, Maria. "Equivariant mappings from vector product into $ G$-spaces of $\varphi $-scalars with $G=O\left( n,1,\mathbb {R}\right) $." Mathematica Bohemica 132.3 (2007): 325-332. <http://eudml.org/doc/250266>.

@article{Glanc2007,
abstract = {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 $\mathbb \{R\}_\{0\}=\left( \mathbb \{R\}\setminus \left\rbrace 0\right\lbrace ,\cdot \right)$.},
author = {Glanc, Barbara, Misiak, Aleksander, Szmuksta-Zawadzka, Maria},
journal = {Mathematica Bohemica},
keywords = {$G$-space; equivariant map; pseudo-Euclidean geometry; -space; equivariant map; pseudo-Euclidean geometry},
language = {eng},
number = {3},
pages = {325-332},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Equivariant mappings from vector product into $ G$-spaces of $\varphi $-scalars with $G=O\left( n,1,\mathbb \{R\}\right) $},
url = {http://eudml.org/doc/250266},
volume = {132},
year = {2007},
}

TY - JOUR
AU - Glanc, Barbara
AU - Misiak, Aleksander
AU - Szmuksta-Zawadzka, Maria
TI - Equivariant mappings from vector product into $ G$-spaces of $\varphi $-scalars with $G=O\left( n,1,\mathbb {R}\right) $
JO - Mathematica Bohemica
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 132
IS - 3
SP - 325
EP - 332
AB - 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 $\mathbb {R}_{0}=\left( \mathbb {R}\setminus \left\rbrace 0\right\lbrace ,\cdot \right)$.
LA - eng
KW - $G$-space; equivariant map; pseudo-Euclidean geometry; -space; equivariant map; pseudo-Euclidean geometry
UR - http://eudml.org/doc/250266
ER -