Biderivations of ${\mathfrak s}{\mathfrak l}(2)$ on All Simple Modules in Prime Characteristic

Abstract

Over an algebraically closed field of characteristic p > 2, this paper gives a sufficient and necessary condition for a map from the Cartesian product of a finite-dimensional Lie algebra with itself two times to its any nontrivial and simple module to be a symmetric biderivation, and determines all biderivations of the 3-dimensional simple Lie algebra ${\mathfrak s}{\mathfrak l}(2)$ on its any finite-dimensional simple module.

Keywords

Biderivations / ${\mathfrak s}{\mathfrak l}(2)$')">${\mathfrak s}{\mathfrak l}(2)$ / simple modules / 17B05 / 17B10 / 17B40 / 17B50

RIGHTS & PERMISSIONS

Peking University