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

## Abstract

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 |
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Subjects: | Mathematics |

Divisions: | SCIENTIFIC PRODUCTION > Mathematics |

Depositing User: | Administrateur Eprints Administrateur Eprints |

Last Modified: | 31 Jan 2020 15:48 |

URI: | http://eprints.umi.ac.ma/id/eprint/3979 |

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