Back to Search
Start Over
Critical groups for Hopf algebra modules
- 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