Critical groups for Hopf algebra modules

Darij Grinberg, J. I.A. Huang, Victor Reiner

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


This paper considers an invariant of modules over a finite-dimensional Hopf algebra, called the critical group. This generalises the critical groups of complex finite group representations studied in [1, 11]. A formula is given for the cardinality of the critical group generally, and the critical group for the regular representation is described completely. A key role in the formulas is played by the greatest common divisor of the dimensions of the indecomposable projective representations.

Original languageEnglish (US)
Pages (from-to)473-503
Number of pages31
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number3
StatePublished - 2020

ASJC Scopus subject areas

  • Mathematics(all)


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