Are we counting or measuring something?

Miriam Cohen, Sara Westreich

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Let H be a semisimple Hopf algebras over an algebraically closed field k of characteristic 0. We define Hopf algebraic analogues of commutators and their generalizations and show how they are related to H ', the Hopf algebraic analogue of the commutator subgroup. We introduce a family of central elements of H ', which on one hand generate H ' and on the other hand give rise to a family of functionals on H. When H = k G, G a finite group, these functionals are counting functions on G. It is not clear yet to what extent they measure any specific invariant of the Hopf algebra. However, when H is quasitriangular they are at least characters on H.

Original languageEnglish
Pages (from-to)111-130
Number of pages20
JournalJournal of Algebra
StatePublished - 15 Jan 2014

Bibliographical note

Funding Information:
This research was supported by the Israel Science Foundation , 170-12 .


  • Commutator algebra
  • Commutators
  • Conjugacy classes
  • Counting functions
  • Generalized commutators
  • Iterated commutators
  • Normalized class sums


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