Local derivations on the Witt algebra in prime characteristic

Abstract

Let $\mathfrak{g}$ be the Witt algebra over an infinite field of prime characteristic p. In this paper, we discuss the properties of local derivations on $\mathfrak{g}$, and prove that every local derivation on $\mathfrak{g}$ is a derivation. Moreover, it is shown that there exist some local derivations which are not derivations for the maximal subalgebra ${\mathfrak{g}}_0$ of $\mathfrak{g}$.

Keywords:

• The Witt algebra
• maximal subalgebra
• derivation
• inner derivation
• local derivation

2010 Mathematics Subject Classifications:

• 17B40
• 17B50
• 17B70

Acknowledgements

The author would like to express his sincere gratitude to the referee for helpful suggestion and comments.

Disclosure statement

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

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (Grant Nos. 12071136, 12271345)