2-local derivations on Witt algebras

TL;DR

This paper proves that all 2-local derivations on Witt algebras and related structures are actual derivations, extending to higher rank centerless generalized Virasoro algebras.

Contribution

It establishes that 2-local derivations on Witt algebras and certain generalized Virasoro algebras are always derivations, a significant structural result.

Findings

Every 2-local derivation on Witt algebras is a derivation.

Extension of the result to higher rank centerless generalized Virasoro algebras.

Applicable to all dimensions, including infinite-dimensional cases.

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.