@inproceedings{298ca4fadd9e4a0696dc8520cf69522b,

title = "Higman ideals and verlinde-type formulas for hopf algebras",

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.",

keywords = "Characters, Conjugacy sums and classes, Factorizable ribbon Hopf algebras, Fusion rules, Hopf algebras, Projective center, Symmetric algebras, Verlinde formula",

author = "Miriam Cohen and Sara Westreich",

note = "Publisher Copyright: {\textcopyright} 2010 Springer Basel AG.; International Conference on Ring and Module Theory, 2008 ; Conference date: 18-08-2008 Through 22-08-2008",

year = "2010",

month = jan,

day = "1",

doi = "10.1007/978-3-0346-0007-1_5",

language = "English",

isbn = "9783034600064",

series = "Trends in Mathematics",

publisher = "Springer International Publishing",

pages = "91--114",

editor = "Toma Albu and Birkenmeier, {Gary F.} and Ali Erdoǧan and Adnan Tercan",

booktitle = "Ring and Module Theory",

}