Critical groups for Hopf algebra modules

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

doi:10.1017/S0305004118000786

Critical groups for Hopf algebra modules

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

Mathematics and Statistics

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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)
Pages (from-to)	473-503
Number of pages	31
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	168
Issue number	3
DOIs	https://doi.org/10.1017/S0305004118000786
State	Published - 2020

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Mathematics(all)

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10.1017/S0305004118000786

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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.",

author = "Darij Grinberg and Huang, {J. I.A.} and Victor Reiner",

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Critical groups for Hopf algebra modules

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