2-local derivations and biderivations of $\mathfrak{sl}(2)$ on all simple modules

Abstract

This paper generalizes the concepts of 2-local derivations and biderivations (without the skewsymmetric condition) of a finite-dimensional Lie algebra from the adjoint module to any finite-dimensional module, and determines all 2-local derivations and biderivations of the 3-dimensional complex simple Lie algebra $\mathfrak{sl}(2)$ on its any finite-dimensional simple module.