Geodesic
Equivariant mappings from vector product into $ G$-spaces of $\varphi $-scalars with $G=O\left( n,1,\mathbb{R}\right) $
Mathematica Bohemica, Tome 132 (2007) no. 3, pp. 325-332.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 $\mathbb{R}_{0}=\left( \mathbb{R}\setminus \left\rbrace 0\right\lbrace ,\cdot \right)$.
DOI : 10.21136/MB.2007.134120
Classification : 53A55
Keywords: $G$-space; equivariant map; pseudo-Euclidean geometry 
@article{10_21136_MB_2007_134120,
     author = {Glanc, Barbara and Misiak, Aleksander and Szmuksta-Zawadzka, Maria},
     title = {Equivariant mappings from vector product into $ G$-spaces of $\varphi $-scalars with $G=O\left( n,1,\mathbb{R}\right) $},
     journal = {Mathematica Bohemica},
     pages = {325--332},
     publisher = {mathdoc},
     volume = {132},
     number = {3},
     year = {2007},
     doi = {10.21136/MB.2007.134120},
     mrnumber = {2355661},
     zbl = {1174.53007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2007.134120/}
}
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
SP  - 325
EP  - 332
VL  - 132
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2007.134120/
DO  - 10.21136/MB.2007.134120
LA  - en
ID  - 10_21136_MB_2007_134120
ER  - 
%0 Journal Article
%A Glanc, Barbara
%A Misiak, Aleksander
%A Szmuksta-Zawadzka, Maria
%T Equivariant mappings from vector product into $ G$-spaces of $\varphi $-scalars with $G=O\left( n,1,\mathbb{R}\right) $
%J Mathematica Bohemica
%D 2007
%P 325-332
%V 132
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2007.134120/
%R 10.21136/MB.2007.134120
%G en
%F 10_21136_MB_2007_134120
Glanc, Barbara; Misiak, Aleksander; 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, Tome 132 (2007) no. 3, pp. 325-332. doi : 10.21136/MB.2007.134120. http://geodesic.mathdoc.fr/articles/10.21136/MB.2007.134120/

Cité par Sources :