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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On derivation algebras of Malcev algebras


Author: Ernest L. Stitzinger
Journal: Proc. Amer. Math. Soc. 62 (1977), 31-33
MSC: Primary 17E05
MathSciNet review: 0424891
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Abstract: It is shown that if A is a Malcev algebra over a field of characteristic 0, then A is semisimple if and only if the derivation algebra $ \mathfrak{D}(A)$ is semisimple. It is then shown that A is semisimple if and only if $ {A^\ast} = \mathfrak{L}(A) + \mathfrak{D}(A)$ is semisimple, where $ \mathfrak{L}(A)$ is the Lie multiplication algebra of A.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0424891-0
PII: S 0002-9939(1977)0424891-0
Article copyright: © Copyright 1977 American Mathematical Society