Higman ideals and verlinde-type formulas for hopf algebras

Miriam Cohen, Sara Westreich

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

9 Scopus citations

Abstract

We offer a comprehensive discussion on Verlinde-type formulas for Hopf algebras H over an algebraically closed field of characteristic 0. Some of the results are new and some are known, but are reproved from the point of view of symmetric algebras and the associated Higman (trace) map. We give an explicit form for the central Casimir element of C(H), which is also known to be χad, the character of the adjoint map on H. We then discuss the following variations of the Verlinde formula: (i) Fusion rules for irreducible characters of semisimple Hopf algebras whose character algebras C(H) are commutative. (ii) Structure constants for what we call here conjugacy sums associated to conjugacy classes for these Hopf algebras. (iii) Equality up to rational scalar multiples between the fusion rules of irreducible characters and the structure constants for semisimple factorizable Hopf algebras. (iv) Projective fusion rules for the multiplication of irreducible and indecomposable projective characters for non-semisimple factorizable Hopf algebras.

Original languageEnglish
Title of host publicationRing and Module Theory
EditorsToma Albu, Gary F. Birkenmeier, Ali Erdoǧan, Adnan Tercan
PublisherSpringer International Publishing
Pages91-114
Number of pages24
ISBN (Print)9783034600064
DOIs
StatePublished - 1 Jan 2010
EventInternational Conference on Ring and Module Theory, 2008 - Ankara, Turkey
Duration: 18 Aug 200822 Aug 2008

Publication series

NameTrends in Mathematics
Volume50
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

Conference

ConferenceInternational Conference on Ring and Module Theory, 2008
Country/TerritoryTurkey
CityAnkara
Period18/08/0822/08/08

Keywords

  • Characters
  • Conjugacy sums and classes
  • Factorizable ribbon Hopf algebras
  • Fusion rules
  • Hopf algebras
  • Projective center
  • Symmetric algebras
  • Verlinde formula

ASJC Scopus subject areas

  • Mathematics (all)

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