Homogeneous O-operators on BiHom-Jordan superalgebras and BiHom-pre-Jordan superalgebras structures

TL;DR

This paper explores the structure and representations of BiHom-Jordan superalgebras, introduces homogeneous O-operators, and establishes connections to BiHom-pre-Jordan superalgebras, advancing the algebraic theory in this area.

Contribution

It introduces the concept of homogeneous O-operators on BiHom-Jordan superalgebras and links them to BiHom-pre-Jordan superalgebra structures, providing new insights and frameworks.

Findings

Defined homogeneous O-operators for BiHom-Jordan superalgebras

Established relationships between BiHom-pre-Jordan and BiHom-Jordan superalgebras

Explored representation and dual representation theories

Abstract

In this paper, we recall the notion of BiHom-generalization of Jordan superalgebras called BiHom-Jordan superalgebras in which, we investigate their representation and associated dual representation theory. We also introduce the notion of homogeneous O-operators of BiHom-Jordan superalgebra associated to a given representation. Additionnaly we define the BiHom-pre-Jordan superalgebras structures, in which we study the relationship between BiHom-pre-Jordan superalgebras and BiHom-Jordan superalgebras via a homogeneous O-operators. Some other related results are considered.