On semisimple Mal′cev algebras

Elduque, Alberto

doi:10.1090/S0002-9939-1989-0979223-4

On semisimple Mal′cev algebras
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Proc. Amer. Math. Soc. 107 (1989), 73-82 Request permission

Abstract:

Let $M$ be a finite dimensional semisimple Malcev algebra over a perfect field of characteristic $\ne 2,3$. Let $N(M)$ be its $J$-nucleus and $J(M,M,M)$ the subspace spanned by its jacobians. Then it is shown that $M = N(M) \oplus J(M,M,M),N(M)$ is a semisimple Lie algebra and $J(M,M,M)$ is a direct sum of simple non-Lie Malcev algebras.

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