On the structure of split involutive Lie algebras

Abstract

We study the structure of arbitrary split involutive Lie algebras. We show that any of such algebras L is of the form L={\mathcal U} +\sum_{j}I_{j} with U a subspace of the involutive abelian Lie subalgebra H and any I_j a well described involutive ideal of L satisfying [I_j,I_k]=0 if j\neq k. Under certain conditions, the simplicity of L is characterized and it is shown that L is the direct sum of the family of its minimal involutive ideals, each one being a simple split involutive Lie algebra.