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Simple Lie color algebras from graded associative algebras

โœ Scribed by Kaiming Zhao

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
232 KB
Volume
269
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

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, : G ร— G โ†’ F * an antisymmetric bicharacter. Suppose A = gโˆˆG A g is a G-graded simple associative algebra over F .

In this paper it is proved that [A, A] /([A, A] โˆฉ Z (A)

) is a simple ( , G)-Lie color algebra if dim Z A > 8, where Z = Z (A) is the color center of A. If A (3) = 0 and dim Z A = 8, then there are two such algebras A such that [A, A] /(Z โˆฉ [A, A] ) is not simple or commutative. This extends a result by Montgomery.

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