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Primeness Criteria for Universal Enveloping Algebras of Lie Color Algebras

✍ Scribed by Kenneth L Price

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
156 KB
Volume
235
Category
Article
ISSN
0021-8693

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✦ Synopsis

We write det L L / 0 q y y if the matrix formed by brackets between elements of a basis of L L is nonsinguy lar. Unlike Lie super algebras, a Lie color algebra L L may have det L L / 0 and a Ž . universal enveloping algebra U L L which is not prime. We will provide examples Ž . and show that U L L is semiprime whenever det L L / 0. Our main theorem is a Ž . Ž . criterion for U L L to be prime. As a corollary, we prove that U L L is prime whenever det L L / 0 and the grading group G is either a finite group whose 2-torsion subgroup is cyclic or a finitely generated group such that for each l Ž l . elementary divisor 2 of G the base field does not contain a primitive 2 th-root of unity.

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