Hom-Jordan-Malcev-Poisson algebras

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 $T^{\ast }$-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.