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Critical groups for Hopf algebra modules

Authors :
Grinberg, Darij
Huang, Jia
Reiner, Victor
Source :
Math. Proc. Camb. Phil. Soc. 168 (2020) 473-503
Publication Year :
2017

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.<br />Comment: 24 pages. Comments are welcome! The ancillary file is a longer version with some more details and alternative proofs (compiled from the same source). The version on http://www.cip.ifi.lmu.de/~grinberg/algebra/ will probably get quicker updates. v3: Minor corrections

Details

Database :
arXiv
Journal :
Math. Proc. Camb. Phil. Soc. 168 (2020) 473-503
Publication Type :
Report
Accession number :
edsarx.1704.03778
Document Type :
Working Paper
Full Text :
https://doi.org/10.1017/S0305004118000786