### Abstract

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 language | English (US) |
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Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

DOIs | |

State | Accepted/In press - 2018 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Grinberg, D. A. R. I. J., Huang, J. I. A., & Reiner, V. (Accepted/In press). Critical groups for Hopf algebra modules.

*Mathematical Proceedings of the Cambridge Philosophical Society*. https://doi.org/10.1017/S0305004118000786