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

Year 2026, Issue: Advanced Online Publication, 1 - 29

Ismail Laraiedh , Sergei Silvestrov

https://doi.org/10.15672/hujms.1417353

Abstract

The purpose of this paper is 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

References

• [1] E. Abdaoui, S. Mabrouk and A. Makhlouf, Rota-Baxter Operators on Pre-Lie Superalgebras, Bull. Malays. Math. Sci. Soc. 42, 1567-1606, 2019.