Higman ideals and Verlinde-type formulas for Hopf algebras

Miriam Cohen, Sara Westreich

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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 χ ad , 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 languageAmerican English
Title of host publicationRing and module theory
EditorsToma Albu, Gary F. Birkenmeier, Ali Erdoğgan, Adnan Tercan
PublisherSpringer Basel
ISBN (Print)978-3-0346-0007-1
StatePublished - 2010

Publication series

NameTrends in Mathematics


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