We present an alternative to existing classifications [see L. Bröcker, Kinematische Räume, Geom. Dedicata 1 (1973) 241--268; H. Karzel, Kinematic spaces, Symposia Mathematica 11 (1973) 413--439] of those quadratic algebras (in the sense of Osborn) which are associative. The alternative consists in studying them as Lie algebras. This generalizes work of J. F. Plebanski and M. Przanowski [Generalizations of the quaternion algebra and Lie algebras, J. Math. Phys. 29 (1988) 529--535], where only algebras over the real and the complex numbers are considered, to algebras over arbitrary fields of characteristic not two; at the same time, considerable simplifications are obtained. The method is not suitable, however, for characteristic two.
1
Institut für Geometrie und Topologie, Universität Stuttgart, 70550 Stuttgart, Germany
2
Liliencronstr. 2, 70619 Stuttgart, Germany
Hermann Hähl; Michael Weller. Classifying Associative Quadratic Algebras of Characteristic not Two as Lie Algebras. Journal of Lie Theory, Tome 19 (2009) no. 3, pp. 543-555. http://geodesic.mathdoc.fr/item/JOLT_2009_19_3_a7/
@article{JOLT_2009_19_3_a7,
author = {Hermann H\"ahl and Michael Weller},
title = {Classifying {Associative} {Quadratic} {Algebras} of {Characteristic} not {Two} as {Lie} {Algebras}},
journal = {Journal of Lie Theory},
pages = {543--555},
year = {2009},
volume = {19},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2009_19_3_a7/}
}
TY - JOUR
AU - Hermann Hähl
AU - Michael Weller
TI - Classifying Associative Quadratic Algebras of Characteristic not Two as Lie Algebras
JO - Journal of Lie Theory
PY - 2009
SP - 543
EP - 555
VL - 19
IS - 3
UR - http://geodesic.mathdoc.fr/item/JOLT_2009_19_3_a7/
ID - JOLT_2009_19_3_a7
ER -
%0 Journal Article
%A Hermann Hähl
%A Michael Weller
%T Classifying Associative Quadratic Algebras of Characteristic not Two as Lie Algebras
%J Journal of Lie Theory
%D 2009
%P 543-555
%V 19
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2009_19_3_a7/
%F JOLT_2009_19_3_a7
