Geodesic
Classifying Associative Quadratic Algebras of Characteristic not Two as Lie Algebras
Journal of Lie theory, Tome 19 (2009) no. 3, pp. 543-555 Cet article a éte moissonné depuis la source Heldermann Verlag

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We present an alternative to existing classifications [see L. Br�cker, Kinematische R�ume, 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.
Classification : 6U99, 17B20, 17B30, 17B60
Mots-clés : Associative quadratic algebra, Lie algebra, nilpotent Lie algebra, solvable Lie algebra, quaternion skew field, classification 
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     author = {H. H�hl and M. 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/JLT_2009_19_3_JLT_2009_19_3_a7/}
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H. H�hl; M. 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/JLT_2009_19_3_JLT_2009_19_3_a7/