Equivariant mappings from vector product into $G$-space of vectors and $\epsilon$-vectors with $G=O(n,1,ℝ)$

Glanc, Barbara, Misiak, Aleksander, and Stepień, Zofia. "Equivariant mappings from vector product into $G$-space of vectors and $\varepsilon $-vectors with $G=O(n,1,\mathbb {R})$." Mathematica Bohemica 130.3 (2005): 265-275. <http://eudml.org/doc/249605>.

@article{Glanc2005,
abstract = {In this note all vectors and $\varepsilon $-vectors of a system of $m\le n$ linearly independent contravariant vectors in the $n$-dimensional pseudo-Euclidean geometry of index one are determined. The problem is resolved by finding the general solution of the functional equation $F( A\{\underset\{1\}\{\rightarrow \}u\}, A\{\underset\{2\}\{\rightarrow \}u\},\dots ,A\{\underset\{m\}\{\rightarrow \}u\}) =( \det A)^\{\lambda \}\cdot A\cdot F( \{\underset\{1\}\{\rightarrow \}u\},\{\underset\{2\}\{\rightarrow \}u\},\dots , \{\underset\{m\}\{\rightarrow \}u\})$ with $\lambda =0$ and $\lambda =1$, for an arbitrary pseudo-orthogonal matrix $A$ of index one and given vectors $ \{\underset\{1\}\{\rightarrow \}u\},\{\underset\{2\}\{\rightarrow \}u\},\dots ,\{\underset\{m\}\{\rightarrow \}u\}.$},
author = {Glanc, Barbara, Misiak, Aleksander, Stepień, Zofia},
journal = {Mathematica Bohemica},
keywords = {$G$-space; equivariant map; pseudo-Euclidean geometry; functional equation; equivariant map; pseudo-Euclidean geometry; functional equation},
language = {eng},
number = {3},
pages = {265-275},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Equivariant mappings from vector product into $G$-space of vectors and $\varepsilon $-vectors with $G=O(n,1,\mathbb \{R\})$},
url = {http://eudml.org/doc/249605},
volume = {130},
year = {2005},
}

TY - JOUR
AU - Glanc, Barbara
AU - Misiak, Aleksander
AU - Stepień, Zofia
TI - Equivariant mappings from vector product into $G$-space of vectors and $\varepsilon $-vectors with $G=O(n,1,\mathbb {R})$
JO - Mathematica Bohemica
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 130
IS - 3
SP - 265
EP - 275
AB - In this note all vectors and $\varepsilon $-vectors of a system of $m\le n$ linearly independent contravariant vectors in the $n$-dimensional pseudo-Euclidean geometry of index one are determined. The problem is resolved by finding the general solution of the functional equation $F( A{\underset{1}{\rightarrow }u}, A{\underset{2}{\rightarrow }u},\dots ,A{\underset{m}{\rightarrow }u}) =( \det A)^{\lambda }\cdot A\cdot F( {\underset{1}{\rightarrow }u},{\underset{2}{\rightarrow }u},\dots , {\underset{m}{\rightarrow }u})$ with $\lambda =0$ and $\lambda =1$, for an arbitrary pseudo-orthogonal matrix $A$ of index one and given vectors $ {\underset{1}{\rightarrow }u},{\underset{2}{\rightarrow }u},\dots ,{\underset{m}{\rightarrow }u}.$
LA - eng
KW - $G$-space; equivariant map; pseudo-Euclidean geometry; functional equation; equivariant map; pseudo-Euclidean geometry; functional equation
UR - http://eudml.org/doc/249605
ER -