Factoriality for the reductive Zassenhaus variety and quantum enveloping algebra |
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Authors: | Amiram Braun |
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Institution: | Dept. of Mathematics, University of Haifa, Haifa, 31905, Israel |
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Abstract: | Let U(g) be the enveloping algebra of a finite dimensional reductive Lie algebra g over an algebraically closed field of prime characteristic. Let U?,P(s:) be the simply connected quantum enveloping algebra at the root of unity ? , of a complex semi-simple finite dimensional Lie algebra s:. We show, by similar proofs, that the centers of both are factorial. While the first result was established by R. Tange 32] (by different methods), the second one confirms a conjecture in 4]. We also provide a general criterion for the factoriality of the centers of enveloping algebras in prime characteristic. |
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Keywords: | Reductive Lie algebras Zassenhaus variety Factoriality Quantum enveloping algebra Prime characteristic |
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