2013/04/03 by Miriam Cohen, Cohen, Miriam, Sara Westreich +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Quantum Algebra (math.QA) #math.QA
paper · pdf · doi:10.48550/arxiv.1304.0968
24 pages
openalex publication_date 2013/04/03 · arxiv created 2013/09/27 · arxiv updated 2013/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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=kG, 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.