On n-Hom-pre-Lie superalgebras structures and their representations

TL;DR

This paper introduces n-Hom-pre-Lie superalgebras, explores their representations, and examines related structures using operators like Rota-Baxter, O-, and Nijenhuis, establishing connections with induced Hom-pre-Lie superalgebras.

Contribution

It defines n-Hom-pre-Lie superalgebras and investigates their representations and structural relationships, expanding the theoretical framework of superalgebra structures.

Findings

Established the structure of n-Hom-pre-Lie superalgebras.

Analyzed representations using Rota-Baxter, O-, and Nijenhuis operators.

Connected n-Hom-pre-Lie superalgebras with induced Hom-pre-Lie superalgebras.

Abstract

In this paper, we introduce the notion of n-Hom-pre-Lie superalgebras. We investigate the representation theory of n-Hom-pre-Lie superalgebras and we give some related results and structures based on Rota-Baxter operators, O-operators and Nijenhuis operators. Moreover, we study relationships between n-Hom-pre-Lie superalgebras and its induced Hom-pre-Lie superalgebras. The same procedure is applied for the representations of n- Hom-pre-Lie superalgebras.