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 Uε,P(s:) be the simply connected quantum enveloping algebra at the root of unity ε, 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.
Original language | English |
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Pages (from-to) | 97-117 |
Number of pages | 21 |
Journal | Advances in Mathematics |
Volume | 274 |
DOIs | |
State | Published - 9 Apr 2015 |
Bibliographical note
Publisher Copyright:© 2015 Elsevier Inc.
Keywords
- Factoriality
- Prime characteristic
- Quantum enveloping algebra
- Reductive Lie algebras
- Zassenhaus variety
ASJC Scopus subject areas
- General Mathematics