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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On semisimple Malcev algebras


Author: Alberto Elduque
Journal: Proc. Amer. Math. Soc. 107 (1989), 73-82
MSC: Primary 17D10
DOI: https://doi.org/10.1090/S0002-9939-1989-0979223-4
MathSciNet review: 979223
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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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DOI: https://doi.org/10.1090/S0002-9939-1989-0979223-4
Keywords: Malcev algebras, $ J$-nucleus, semisimple, Lie algebras
Article copyright: © Copyright 1989 American Mathematical Society