Journal of Lie Theory

no. 3
Classifying Associative Quadratic Algebras of Characteristic not Two as Lie Algebras
Hermann Hähl1; Michael Weller2
1Institut für Geometrie und Topologie, Universität Stuttgart, 70550 Stuttgart, Germany
2Liliencronstr. 2, 70619 Stuttgart, Germany
Journal of Lie Theory, Volume 19 (2009) no. 3, pp. 543-555
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.
DOI: 10.5802/jolt.569
Classification: 6U99, 17B20, 17B30, 17B60
Keywords: Associative quadratic algebra, Lie algebra, nilpotent Lie algebra, solvable Lie algebra, quaternion skew field, classification

Hermann Hähl  1 ; Michael Weller  2

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, Volume 19 (2009) no. 3, pp. 543-555. doi: 10.5802/jolt.569
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     title = {Classifying {Associative} {Quadratic} {Algebras} of {Characteristic} not {Two} as {Lie} {Algebras}},
     journal = {Journal of Lie Theory},
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