# Critical groups for Hopf algebra modules

D. A.R.I.J. Grinberg, J. I.A. Huang, Victor Reiner

Research output: Contribution to journalArticle

### 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) Mathematical Proceedings of the Cambridge Philosophical Society https://doi.org/10.1017/S0305004118000786 Accepted/In press - Jan 1 2018

### Fingerprint

Critical Group
Hopf Algebra
Module
Projective Representation
Highest common factor
Group Representation
Finite Dimensional Algebra
Cardinality
Finite Group
Generalise
Invariant

### 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.

In: Mathematical Proceedings of the Cambridge Philosophical Society, 01.01.2018.

Research output: Contribution to journalArticle

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