Abstract
In this paper, a complete generalization of Herstein's theorem to the case of Lie color algebras is obtained. Let G be an abelian group, F a field of characteristic not 2, ϵ :G×G→F ∗ an anti-symmetric bicharacter. Suppose A =⊕ g ∈ G A g is a G -graded simple associative algebra over F . In this paper it is proved that [ A , A ] ϵ /([ A , A ] ϵ ∩ Z ϵ ( A )) is a simple ( ϵ , G )-Lie color algebra if dim Z ϵ A >8, where Z ϵ = Z ϵ ( A ) is the color center of A . If A (3) ≠0 and dim Z ϵ A =8, then there are two such algebras A such that [ A , A ] ϵ /( Z ϵ ∩[ A , A ] ϵ ) is not simple or commutative. This extends a result by Montgomery.
Published Version
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