Super Kupershmidt Operators on Pre-Malcev Superalgebras

The main purpose of this paper is to study a generalization of pre-Malcev algebras and pre-Lie superalgebras, which is called pre-Malcev superalgebras. We first introduce the definition of pre-Malcev superalgebras with representations, and obtain some important properties and constructions of the super Kupershmidt operators on pre-Malcev superalgebras. Then we give the relationship among pre-Malcev superalgebras, alternative superalgebras and M-dendriform superalgebras. Furthermore, we give infinitesimal deformations of super Kupershmidt operators. Finally, we define bimodules of pre-Malcev superalgebras and study their relationships with super Kupershmidt operators.