Factoriality for the reductive Zassenhaus variety and quantum enveloping algebra

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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 languageEnglish
Pages (from-to)97-117
Number of pages21
JournalAdvances in Mathematics
StatePublished - 9 Apr 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc.


  • Factoriality
  • Prime characteristic
  • Quantum enveloping algebra
  • Reductive Lie algebras
  • Zassenhaus variety

ASJC Scopus subject areas

  • General Mathematics


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