Mathematica Eterna
Open Access

Abstract

Lie algebras with idempotent derivations

BAI Ruipu, GAO Yansha and LI Zhengheng

The structure of Lie algebras with idempotent derivations is studied. It is proved that a Lie algebra L has an idempotent derivation D if and only if L = I ⊕ K, where I is an abelian ideal which is the image of D, K is a subalgebra of L which is the kernel of D, and D is identity on I.