ON THE STRUCTURE OF SPLIT INVOLUTIVE LIE ALGEBRAS

摘要

We study the structure of arbitrary split involutive Lie algebras. We show that any of such algebras L is of the form L = u + Sigma(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 not equal 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.