Split Malcev algebras

Abstract

We study the structure of split Malcev algebras of arbitrary dimension over an algebraically closed field of characteristic zero. We show that any such algebras M is of the form \(M={\mathcal U} +\sum_{j}I_{j}\) with \({\mathcal U}\) a subspace of the abelian Malcev subalgebra H and any Ij a well described ideal of M satisfying [Ij,Ik] = 0 if j ≠ k. Under certain conditions, the simplicity of M is characterized and it is shown that M is the direct sum of a semisimple split Lie algebra and a direct sum of simple non-Lie Malcev algebras.