Some computations of Frobenius-Schur indicators of the regular representations of Hopf algebras

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We study Frobenius-Schur indicators of the regular representations of finite-dimensional semisimple Hopf algebras, especially group-theoretical ones. Those of various Hopf algebras are computed explicitly. In view of our computational results, we formulate the theorem of Frobenius for semisimple Hopf algebras and give some partial results on this problem.

Original languageEnglish
Pages (from-to)325-357
Number of pages33
JournalAlgebras and Representation Theory
Volume15
Issue number2
DOIs
Publication statusPublished - 2012 Apr
Externally publishedYes

Keywords

  • Frobenius-Schur indicator
  • Fusion category
  • Hopf algebra

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Some computations of Frobenius-Schur indicators of the regular representations of Hopf algebras. / Shimizu, Kenichi.

In: Algebras and Representation Theory, Vol. 15, No. 2, 04.2012, p. 325-357.

Research output: Contribution to journalArticle

@article{9c95f252c2d84d04b768d701c6be51c4,
title = "Some computations of Frobenius-Schur indicators of the regular representations of Hopf algebras",
abstract = "We study Frobenius-Schur indicators of the regular representations of finite-dimensional semisimple Hopf algebras, especially group-theoretical ones. Those of various Hopf algebras are computed explicitly. In view of our computational results, we formulate the theorem of Frobenius for semisimple Hopf algebras and give some partial results on this problem.",
keywords = "Frobenius-Schur indicator, Fusion category, Hopf algebra",
author = "Kenichi Shimizu",
year = "2012",
month = "4",
doi = "10.1007/s10468-010-9243-5",
language = "English",
volume = "15",
pages = "325--357",
journal = "Algebras and Representation Theory",
issn = "1386-923X",
publisher = "Springer Netherlands",
number = "2",

}

TY - JOUR

T1 - Some computations of Frobenius-Schur indicators of the regular representations of Hopf algebras

AU - Shimizu, Kenichi

PY - 2012/4

Y1 - 2012/4

N2 - We study Frobenius-Schur indicators of the regular representations of finite-dimensional semisimple Hopf algebras, especially group-theoretical ones. Those of various Hopf algebras are computed explicitly. In view of our computational results, we formulate the theorem of Frobenius for semisimple Hopf algebras and give some partial results on this problem.

AB - We study Frobenius-Schur indicators of the regular representations of finite-dimensional semisimple Hopf algebras, especially group-theoretical ones. Those of various Hopf algebras are computed explicitly. In view of our computational results, we formulate the theorem of Frobenius for semisimple Hopf algebras and give some partial results on this problem.

KW - Frobenius-Schur indicator

KW - Fusion category

KW - Hopf algebra

UR - http://www.scopus.com/inward/record.url?scp=84862124823&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862124823&partnerID=8YFLogxK

U2 - 10.1007/s10468-010-9243-5

DO - 10.1007/s10468-010-9243-5

M3 - Article

VL - 15

SP - 325

EP - 357

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

SN - 1386-923X

IS - 2

ER -