Local derivations on Witt 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.

Keywords:

• Lie algebra
• Witt algebra
• generalized Virasoro algebra
• derivation
• local derivation

AMS Subject Classifications:

• 17B05
• 17B40
• 17B66

Acknowledgments

This research is partially supported by NSFC (11871190) and NSERC (311907-2015). The authors are grateful to the referee for some good suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is partially supported by National Natural Science Foundation of China (NSFC) (Grant Number 11871190) and Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada (NSERC) (Grant Number 311907-2015).