Representations and relative Rota-Baxter operators of Hom-Leibniz Poisson algebras

TL;DR

This paper introduces and studies representations and relative Rota-Baxter operators of Hom-Leibniz Poisson algebras, providing characterizations and exploring related structures like matched pairs and Nijenhuis operators.

Contribution

It presents new concepts and characterizations for Rota-Baxter operators and related structures in Hom-Leibniz Poisson algebras, expanding the theoretical framework.

Findings

Characterizations of relative Rota-Baxter operators

Definitions of matched pairs and Nijenhuis operators

Construction methods for Hom-Leibniz Poisson algebras

Abstract

Representations and relative Rota-Baxter operators with respect to representations of Hom-Leibniz Poisson algebras are introduced and studied. Some characterizations of these operators are obtained. The notion of matched pair and Nijenhuis operators of Hom-Leibniz Poisson algebras are given and various relevant constructions of these Hom-algebras are deduced.