Cherednik, Hecke and quantum algebras as free Frobenius and Calabi-Yau extensions

K. A. Brown, I. G. Gordon, C. H. Stroppel

Research output: Contribution to journalArticlepeer-review

Abstract

We show how the existence of a PBW-basis and a large enough central subalgebra can be used to deduce that an algebra is Frobenius. We apply this to rational Cherednik algebras, Hecke algebras, quantised universal enveloping algebras, quantum Borels and quantised function algebras. In particular, we give a positive answer to [R. Rouquier, Representations of rational Cherednik algebras, in: Infinite-Dimensional Aspects of Representation Theory and Applications, Amer. Math. Soc., 2005, pp. 103-131] stating that the restricted rational Cherednik algebra at the value t = 0 is symmetric. (c) 2007 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)1007-1034
Number of pages28
JournalInternational Electronic Journal of Algebra
Volume319
Issue number3
DOIs
Publication statusPublished - 1 Feb 2008

Keywords

  • Frobenius algebras
  • Calabi-Yau algebras
  • quantum groups
  • Hecke algebras
  • rational Cherednik algebras
  • SYMPLECTIC REFLECTION ALGEBRAS
  • DUALIZING COMPLEXES
  • REPRESENTATION-THEORY
  • PRIMITIVE-IDEALS
  • HOPF-ALGEBRAS
  • ROOTS
  • MODULES
  • RINGS

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