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

Kenichi Shimizu

doi:10.1007/s10468-010-9243-5

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

Kenichi Shimizu

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

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 language	English
Pages (from-to)	325-357
Number of pages	33
Journal	Algebras and Representation Theory
Volume	15
Issue number	2
DOIs	https://doi.org/10.1007/s10468-010-9243-5
Publication status	Published - 2012 Apr
Externally published	Yes

Keywords

Frobenius-Schur indicator
Fusion category
Hopf algebra

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s10468-010-9243-5

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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.",

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author = "Kenichi Shimizu",

note = "Funding Information: Acknowledgements The author is grateful to Professor Mitsuhiro Takeuchi for his valuable comments on Sections 2 and 3. This work is supported by Grant-in-Aid for JSPS Fellows (21 · 2147). Copyright: Copyright 2012 Elsevier B.V., All rights reserved.",

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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.

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KW - Hopf algebra

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

Abstract

Keywords

ASJC Scopus subject areas

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