Transposed Hom-Poisson and Hom-pre-Lie Poisson algebras

Abstract

The purpose of this paper is to introduce and give some constructions results and examples of transposed Hom-Poisson and Hom-pre-Lie Poisson algebras. Also, we establish the bimodules and matched pairs of transposed Hom-Poisson algebras. Their related relevant properties are also given. Finally, the notion of $\mathcal{O}$-operator is exploited to establish the relations between transposed Hom-Poisson and Hom-pre-Lie Poisson algebras.

Keywords

• transposed Hom-Poisson algebra
• Hom-pre-LiePoisson algebra
• bimodule
• $\mathcal{O}$-operator

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