Journal of Lie Theory

no. 3
Classifying Associative Quadratic Algebras of Characteristic not Two as Lie Algebras
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 
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     author = {H. H\"ahl 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},
     doi = {10.5802/jolt.569},
     zbl = {1233.17006},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.569/}
}
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H. Hähl; M. 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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