2-local derivations on the Jacobson-Witt algebras in prime characteristic

Abstract

This paper initiates the study of 2-local derivations on Lie algebras over fields of prime characteristic. Let g be a simple Jacobson-Witt algebra W n over a field of prime characteristic p with cardinality no less than p n . In this paper, we study properties of 2-local derivations on g, and show that every 2-local derivation on g is a derivation.