2-Local derivations on generalized Witt algebras

Abstract

In the present paper, we study 2-local derivations on the so-called infinite dimensional generalized Witt algebras. Firstly, we prove that every 2-local derivation on the generalized Witt algebra over the vector space is a derivation, where is a field of characteristic zero. Further we consider generalized Witt algebras of the form over the field , where I is an infinite index set and and prove that all 2-local derivations on are also derivations. Finally, we show that every 2-local derivation on the Borel subalgebra of is a derivation.