local derivations on Witt algebras

TL;DR

This paper proves that all local derivations on Witt algebras and certain related algebras are actual derivations, extending the understanding of their algebraic structure and symmetries.

Contribution

It establishes that every local derivation on Witt algebras and higher rank centerless generalized Virasoro algebras is a derivation, confirming a conjecture in this area.

Findings

All local derivations on Witt algebras are derivations.

Extension of results to higher rank centerless generalized Virasoro algebras.

Provides a comprehensive characterization of local derivations in these algebras.

Abstract

In this paper, we prove that every local derivation on Witt algebras $W_n, W_n^+$ or $W_n^{++} $ is a derivation for any $n\in\mathbb{N}$. As a consequence, we obtain that every local derivation on a centerless generalized Virasoro algebra of higher rank is a derivation.