Triple derivations on parabolic subalgebras of Kac-Moody algebras

Abstract

A linear map on a Lie algebra is called a triple derivation if for all Let be a Kac-Moody algebra over an algebraically closed field of characteristic 0, and an arbitrary parabolic subalgebra of In this paper, we prove that any triple derivation of is a derivation, which generalizes the corresponding existing result for finite-dimensional simple Lie algebra.