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 $\mathfrak{g}$.

中文翻译：

---

素数特征中 Witt 代数的局部推导

让$\mathfrak{G}$是素数特征p的无限域上的 Witt 代数。在本文中，我们讨论了局部导数的性质$\mathfrak{G}$, 并证明每个局部推导$\mathfrak{G}$是一个推导。此外，证明了存在一些局部推导，这些推导不是最大子代数的推导${\mathfrak{G}}_0$的$\mathfrak{G}$.