Ait Ben Haddou, M. and Benayadi, S. and Boulmane, S. (2016) Malcev-Poisson-Jordan algebras. Journal of Algebra and its Applications, 15 (9).

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Malcev-Poisson-Jordan algebra (MPJ-algebra) is defined to be a vector space endowed with a Malcev bracket and a Jordan structure which are satisfying the Leibniz rule. We describe such algebras in terms of a single bilinear operation, this class strictly contains alternative algebras. For a given Malcev algebra (P, ,), it is interesting to classify the Jordan structure on the underlying vector space of P such that (P, ,,) is an MPJ-algebra ( is called an MPJ-structure on Malcev algebra (P, ,)). In this paper we explicitly give all MPJ-structures on some interesting classes of Malcev algebras. Further, we introduce the concept of pseudo-Euclidean MPJ-algebras (PEMPJ-algebras) and we show how one can construct new interesting quadratic Lie algebras and pseudo-Euclidean Malcev (non-Lie) algebras from PEMPJ-algebras. Finally, we give inductive descriptions of nilpotent PEMPJ-algebras. © 2016 World Scientific Publishing Company.

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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