Triple derivations on parabolic subalgebras of Kac-Moody algebras

Abstract

A linear map $\phi$ on a Lie algebra $\mathfrak{g}$ is called a triple derivation if $\phi ([[x,y],z])=[[\phi (x),y],z]+[[x,\phi (y)],z]+[[x,y],\phi (z)]$ for all $x,y,z\in \mathfrak{g}.$ Let $\mathfrak{g}$ be a Kac-Moody algebra over an algebraically closed field of characteristic 0, and $\mathfrak{p}$ an arbitrary parabolic subalgebra of $\mathfrak{g}.$ In this paper, we prove that any triple derivation of $\mathfrak{p}$ is a derivation, which generalizes the corresponding existing result for finite-dimensional simple Lie algebra.

Keywords:

• Lie triple derivations
• derivations
• parabolic subalgebras
• Kac–Moody algebras

2020 Mathematics Subject Classification:

• 17B05
• 17B40
• 17B67

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (Grant No. 11871014) and the Fujian Province Nature Science Foundation (No. 2020J01162).