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

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1017/S0305004118000786

Cite this

@article{b7d73d730e0d43c6bacf2d9637bb4de1,

title = "Critical groups for Hopf algebra modules",

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",

note = "Publisher Copyright: Copyright {\textcopyright} Cambridge Philosophical Society 2018.",

year = "2020",

doi = "10.1017/S0305004118000786",

language = "English (US)",

volume = "168",

pages = "473--503",

journal = "Mathematical Proceedings of the Cambridge Philosophical Society",

issn = "0305-0041",

publisher = "Cambridge University Press",

number = "3",

}

TY - JOUR

T1 - Critical groups for Hopf algebra modules

AU - Grinberg, Darij

AU - Huang, J. I.A.

AU - Reiner, Victor

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85056298535&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85056298535&partnerID=8YFLogxK

U2 - 10.1017/S0305004118000786

DO - 10.1017/S0305004118000786

M3 - Article

AN - SCOPUS:85056298535

SN - 0305-0041

VL - 168

SP - 473

EP - 503

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

IS - 3

ER -

Critical groups for Hopf algebra modules

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this