Hom–Jordan–Malcev–Poisson algebras
DOI:
https://doi.org/10.37863/umzh.v74i11.6360Keywords:
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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