On derivation algebras of Malcev algebras

Stitzinger, Ernest L.

doi:10.1090/S0002-9939-1977-0424891-0

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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