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arXiv · 1704.03778

Critical groups for Hopf algebra modules

Darij Grinberg·Jia Huang·Victor Reiner
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Abstract

This paper considers an invariant of modules over a finite-dimensional Hopf algebra, called the critical group. This generalizes the critical groups of complex finite group representations studied by Benkart, Klivans, Reiner and Gaetz. 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.

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BibTeXRIS

Darij Grinberg, Jia Huang, Victor Reiner. 2026-06-13. Critical groups for Hopf algebra modules. https://doi.org/10.1017/s0305004118000786

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