
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 D ( A ) \mathfrak {D}(A) is semisimple. It is then shown that A is semisimple if and only if A ∗ = L ( A ) + D ( A ) {A^\ast } = \mathfrak {L}(A) + \mathfrak {D}(A) is semisimple, where L ( A ) \mathfrak {L}(A) is the Lie multiplication algebra of A.
Nonassociative algebras satisfying other identities
Nonassociative algebras satisfying other identities
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