Structure constants related to symmetric Hopf algebras

Miriam Cohen, Sara Westreich

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Let k be an algebraically closed field of characteristic 0. In this paper we continue our study of structure constants for semisimple Hopf algebras H whose character algebra is commutative, and for non-semisimple factorizable ribbon Hopf algebras. This is done from the point of view of symmetric algebras, such as group algebras. In particular we consider general fusion rules which are structure constants associated to products of irreducible characters and structure constants associated to generalizations of class sums and conjugacy classes. Our methods are reminiscent on one hand of the methods employed when analyzing tilting modules for certain quantum groups and on the other hand of "splitting modules" for certain Drinfeld doubles. The family of irreducible characters is divided in two according to the vanishing of their quantum dimension. The fusion rules on the character algebra are computed with respect to this division.

Original languageEnglish
Pages (from-to)3219-3240
Number of pages22
JournalJournal of Algebra
Volume324
Issue number11
DOIs
StatePublished - 1 Dec 2010

Keywords

  • Algebras
  • Characters
  • Factorizable ribbon Hopf algebras
  • Fusion rules
  • Symmetric Hopf algebras

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint

Dive into the research topics of 'Structure constants related to symmetric Hopf algebras'. Together they form a unique fingerprint.

Cite this