On Hom-Nambu-Poisson superalgebras structures and their representations

TL;DR

This paper explores the construction and representation of Hom-Nambu-Poisson superalgebras, introducing n-ary structures and examining their relationships with Hom-Poisson superalgebras, using tools like Rota-Baxter operators.

Contribution

It introduces n-ary Hom-Nambu-Poisson superalgebras and their representations, expanding the framework of Hom-Poisson superalgebras and their interrelations.

Findings

Defined n-ary Hom-Nambu-Poisson superalgebras and their representations

Established relationships between Hom-Poisson and n-ary Hom-Nambu structures

Analyzed the role of Rota-Baxter operators in these constructions

Abstract

The purpose of this paper is to study some results of constructions on Hom-Poisson superal-gebras we use the representations and Rota-Baxter operators. We introduce the structures ofn-ary Hom-Nambu Poisson superalgebras and their representations and we study relationships between Hom-Poissonsuperalgebras and its inducedn-ary Hom-Nambu Poisson superalgebras. The same concept is given for therepresentations ofn-ary Hom-Nambu Poisson superalgebras.