Pseudo-Euclidean Alternative Algebras
2016; Taylor & Francis; Volume: 44; Issue: 12 Linguagem: Inglês
10.1080/00927872.2016.1149187
ISSN1532-4125
AutoresMalika Ait Ben Haddou, Said Boulmane,
Tópico(s)Finite Group Theory Research
ResumoIn this paper, we transfer the notion of double extension, introduced by Medina and Revoy for quadratic Lie algebras [8 Medina, A., Revoy, Ph. (1985). Algèbre de Lie et produit scalaire invariant. Ann. Sci. Ecole Norm. Sup. (4) 18(3):553–561. [Google Scholar]], and extended by Benayadi and Baklouti for pseudo-euclidean Jordan algebras [1 Baklouti, A., Benayadi, S. (2015). Pseudo-euclidean Jordan algebras. Comm. in. Alg. 43(5):2094–2123.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar], 2 Baklouti, A. (2007). Structures et descriptions inductives des algèbres de Jordan pseudo-euclidiennes. Thèse. Université Paul Verlaine-Metz. [Google Scholar]], to the case of pseudo-euclidean alternative algebras. We show that every pseudo-euclidean alternative algebra, which is irreducible and neither simple nor nilpotent, is a suitable double extension. Moreover, we introduce the notion of generalized double extension of pseudo-euclidean alternative algebras by the one dimensional alternative algebra with zero product. This leads to an inductive classification of nilpotent pseudo-euclidean alternative algebras. A short review of the basics on alternative algebras and their connections to some other algebraic structures is also provided.
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