Equivariant maps between certain $G$-spaces with $G=O(n-1,1)$.

Misiak, Aleksander, and Stasiak, Eugeniusz. "Equivariant maps between certain $G$-spaces with $G=O( n-1,1)$.." Mathematica Bohemica 126.3 (2001): 555-560. <http://eudml.org/doc/248881>.

@article{Misiak2001,
abstract = {In this note, there are determined all biscalars of a system of $s\le n$ linearly independent contravariant vectors in $n$-dimensional pseudo-Euclidean geometry of index one. The problem is resolved by finding a general solution of the functional equation $F(A\{\underset\{1\}\{\rightarrow \}u\},A \{\underset\{2\}\{\rightarrow \}u\},\dots ,A\{\underset\{s\}\{\rightarrow \}u\}) =( \text\{sign\}( \det A)) F (\{\underset\{1\}\{\rightarrow \}u\},\{\underset\{2\}\{\rightarrow \}u\},\dots ,\{\underset\{s\}\{\rightarrow \}u\}) $ for an arbitrary pseudo-orthogonal matrix $A$ of index one and the given vectors $\{\underset\{1\}\{\rightarrow \}u\}, \{\underset\{2\}\{\rightarrow \}u\},\dots ,\{\underset\{s\}\{\rightarrow \}u\}$.},
author = {Misiak, Aleksander, Stasiak, Eugeniusz},
journal = {Mathematica Bohemica},
keywords = {$G$-space; equivariant map; vector; scalar; biscalar; -space; equivariant map; vector; scalar; biscalar},
language = {eng},
number = {3},
pages = {555-560},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Equivariant maps between certain $G$-spaces with $G=O( n-1,1)$.},
url = {http://eudml.org/doc/248881},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Misiak, Aleksander
AU - Stasiak, Eugeniusz
TI - Equivariant maps between certain $G$-spaces with $G=O( n-1,1)$.
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 3
SP - 555
EP - 560
AB - In this note, there are determined all biscalars of a system of $s\le n$ linearly independent contravariant vectors in $n$-dimensional pseudo-Euclidean geometry of index one. The problem is resolved by finding a general solution of the functional equation $F(A{\underset{1}{\rightarrow }u},A {\underset{2}{\rightarrow }u},\dots ,A{\underset{s}{\rightarrow }u}) =( \text{sign}( \det A)) F ({\underset{1}{\rightarrow }u},{\underset{2}{\rightarrow }u},\dots ,{\underset{s}{\rightarrow }u}) $ for an arbitrary pseudo-orthogonal matrix $A$ of index one and the given vectors ${\underset{1}{\rightarrow }u}, {\underset{2}{\rightarrow }u},\dots ,{\underset{s}{\rightarrow }u}$.
LA - eng
KW - $G$-space; equivariant map; vector; scalar; biscalar; -space; equivariant map; vector; scalar; biscalar
UR - http://eudml.org/doc/248881
ER -