Ait Ben Haddou, M. and Boulmane, S. (2016) Pseudo-Euclidean Alternative Algebras. Communications in Algebra, 44 (12). pp. 5199-5222.

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In this paper, we transfer the notion of double extension, introduced by Medina and Revoy for quadratic Lie algebras 8, and extended by Benayadi and Baklouti for pseudo-euclidean Jordan algebras 1, 2, 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. © 2016, Copyright © Taylor & Francis Group, LLC.

Item Type: Article
Subjects: Mathematics
Divisions: SCIENTIFIC PRODUCTION > Mathematics
Depositing User: Administrateur Eprints Administrateur Eprints
Last Modified: 31 Jan 2020 15:48

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