Super-Biderivations and Linear Super-Commuting Maps on the Lie Superalgebras

TL;DR

This paper explores the relationships between linear super-commuting maps, super-biderivations, and centroids in Lie superalgebras, extending previous algebraic results to a broader superalgebra context.

Contribution

It generalizes existing results on Lie algebras to Lie superalgebras, describing their intrinsic connections under specific assumptions.

Findings

Established connections among super-commuting maps, super-biderivations, and centroids.

Extended classical Lie algebra results to Lie superalgebras.

Provided a framework for understanding superalgebra structures in algebraically closed fields.

Abstract

Suppose the ground field is algebraically closed and of characteristic different from 2. In this paper, we described the intrinsic connections among linear super-commuting maps, super-biderivations and centroids for Lie superalgebras satisfying certain assumptions. This is a generalization of the results of Bre$\check{s}$ar and Zhao on Lie algebras.