Local derivations on Borel subalgebras of finite-dimensional simple Lie algebras

Abstract

Let $\mathbb{F}$ be an algebraically closed field of characteristic 0, let $\mathcal{L}$ be a finite-dimensional simple Lie algebra over $\mathbb{F}$, and let $\mathcal{B}$ be the standard Borel subalgebra of $\mathcal{L}$. In this paper we prove that every local derivation of $\mathcal{B}$ is a derivation.

Keywords:

• Local derivations
• Borel subalgebras
• finite-dimensional simple Lie algebras

2010 Mathematics Subject Classification:

• 17B20
• 17B40

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (Grant No. 11871014, 11571360) and the Fujian Province Nature Science Foundation (No. 2016J01006 and JZ160427).