Are we counting or measuring something?

Miriam Cohen, Sara Westreich

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

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
Volume398
DOIs
StatePublished - 15 Jan 2014

Bibliographical note

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

Funding

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

FundersFunder number
Israel Science Foundation170-12

    Keywords

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

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