Hom-Jordan-Malcev-Poisson algebras

TL;DR

This paper introduces and studies Hom-Jordan-Malcev-Poisson algebras, a Hom-type generalization of classical algebraic structures, exploring their properties, classifications, and relationships with related systems.

Contribution

It defines Hom-Jordan-Malcev-Poisson algebras, analyzes their closure properties, characterizes admissible cases, and extends related concepts like pseudo-Euclidian and Lie-Jordan-Poisson systems to the Hom setting.

Findings

Hom-Jordan-Malcev-Poisson algebras are closed under suitable twisting.

Characterization of admissible Hom-Jordan-Malcev-Poisson algebras provided.

Extension of Lie-Jordan-Poisson triple systems to the Hom framework.

Abstract

The purpose of this paper is to provide and study a Hom-type generalization of Jordan-Malcev-Poisson algebras, called Hom-Jordan-Malcev-Poisson algebras. We show that they are closed under twisting by suitable self-maps and give a characterization of admissible Hom-Jordan-Malcev-Poisson algebras. In addition, we introduce the notion of pseudo-Euclidian Hom-Jordan-Malcev-Poisson algebras and describe its $T^*$-extension. Finally, we generalize the notion of Lie-Jordan-Poisson triple system to the Hom setting and establish its relationships with Hom-Jordan-Malcev-Poisson algebras.