Local properties of Jacobson-Witt algebras (Q2049412)

The derivation algebra of an algebra plays an important role to the study of the structure of the algebra. As a generalization of derivation, the concept of 2-local derivation is actually an important and interesting property for an algebra. The paper under review initiates the study on 2-local derivations of Lie algebras of prime characteristic. More precisely, it is shown that 2-local derivations on a simple Jacobson-Witt algebra over a field of prime characteristic are derivations under mild restriction on the cardinality of the field. For the nonsimple case, there exist a 2-local derivation that is not a derivation.