Characters and a Verlinde-type formula for symmetric Hopf algebras

Miriam Cohen, Sara Westreich

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


We study certain aspects of finite-dimensional non-semisimple symmetric Hopf algebras H and their duals H*. We focus on the set I (H) of characters of projective H-modules which is an ideal of the algebra of cocommutative elements of H*. This ideal corresponds via a symmetrizing form to the projective center (Higman ideal) of H which turns out to be Λ H, where Λ is an integral of H and {A figure is presented} is the left adjoint action of H on itself. We describe Λ H via primitive and central primitive idempotents of H. We also show that it is stable under the quantum Fourier transform. Our best results are obtained when H is a factorizable ribbon Hopf algebra over an algebraically closed field of characteristic 0. In this case Λ H is also the image of I (H) under a "translated" Drinfel'd map. We use this fact to prove the existence of a Steinberg-like character. The above ingredients are used to prove a Verlinde-type formula for Λ H.

Original languageEnglish
Pages (from-to)4300-4316
Number of pages17
JournalJournal of Algebra
Issue number12
StatePublished - 15 Dec 2008


  • Characters
  • Factorizable ribbon Hopf algebras
  • Symmetric algebras
  • Unimodular Hopf algebras

ASJC Scopus subject areas

  • Algebra and Number Theory


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