### 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) |
---|---|

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

DOIs | |

Publication status | Accepted/In press - Jan 1 2018 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Critical groups for Hopf algebra modules.** / Grinberg, D. A.R.I.J.; Huang, J. I.A.; Reiner, Victor.

Research output: Contribution to journal › Article