Hom–Jordan–Malcev–Poisson algebras

T.  Chtioui; S.  Mabrouk; A.  Makhlouf

doi:10.37863/umzh.v74i11.6360

T. Chtioui Univ. Sfax, Tunisia
S. Mabrouk Univ. Gafsa, Tunisia
A. Makhlouf Univ. de Haute Alsace, IRIMAS, Mulhouse, France

DOI: https://doi.org/10.37863/umzh.v74i11.6360

Keywords: Hom-JMP-algebra, Hom-Malcev algebra, Hom-Jordan algebra, Hom-flexible algebras, admissible Hom-JMP algebra, Pseudo-Euclidian Hom-JMP algebra, Hom-Lie-Jordan-Poisson triple system.

Abstract

UDC 512.5

We 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.

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