On Hom–Nambu–Poisson superalgebras structures and their representations

Abstract

The purpose of this paper is to study some results of constructions on Hom–Poisson superalgebras. We use the representations and Rota–Baxter operators. We introduce the notion of [Formula: see text]-ary Hom–Nambu–Poisson superalgebras and their representations and we study relationships between Hom–Poisson superalgebras and its induced [Formula: see text]-ary Hom–Nambu–Poisson superalgebras. The same concept is applied for the representations of [Formula: see text]-ary Hom–Nambu–Poisson superalgebras.