2-local derivations on Witt algebras

Abstract

In this paper, we prove that every 2-local derivation on Witt algebras $W_n,W_n^{+}$ or $W_n^{++}$ is a derivation for all $n=1,2,\cdots ,\infty$. As a consequence we obtain that every 2-local derivation on any centerless generalized Virasoro algebra of higher rank is a derivation.

9 pages