On derivation algebras of Malcev algebras
Author:
Ernest L. Stitzinger
Journal:
Proc. Amer. Math. Soc. 62 (1977), 31-33
MSC:
Primary 17E05
DOI:
https://doi.org/10.1090/S0002-9939-1977-0424891-0
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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Article copyright:
© Copyright 1977
American Mathematical Society