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

TL;DR

This paper extends the study of 2-local derivations and biderivations from the adjoint module to all finite-dimensional modules of the simple Lie algebra rak{sl}(2), providing a complete classification.

Contribution

It generalizes the concepts of 2-local derivations and biderivations to arbitrary modules and classifies all such derivations for rak{sl}(2) on its simple modules.

Findings

All 2-local derivations of rak{sl}(2) on simple modules are characterized.

All biderivations of rak{sl}(2) on simple modules are classified.

The results extend previous work limited to the adjoint module.

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 $\frak{sl}(2)$ on its any finite-dimensional simple module.