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

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.