Frobenius-Schur indicators in Tambara-Yamagami categories

Kenichi Shimizu

doi:10.1016/j.jalgebra.2011.02.002

Frobenius-Schur indicators in Tambara-Yamagami categories

Kenichi Shimizu

Department of Mathematical Sciences

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

10 Citations (Scopus)

Abstract

We introduce formulae of Frobenius-Schur indicators of simple objects of Tambara-Yamagami categories. By using techniques of the Fourier transform on finite abelian groups, we study some arithmetic properties of indicators. We also give some applications to Hopf algebras.

Original language	English
Pages (from-to)	543-564
Number of pages	22
Journal	Journal of Algebra
Volume	332
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2011.02.002
Publication status	Published - 2011 Apr 15

Keywords

Frobenius-Schur indicator
Fusion category
Hopf algebra
Tambara-Yamagami category

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1016/j.jalgebra.2011.02.002

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title = "Frobenius-Schur indicators in Tambara-Yamagami categories",

abstract = "We introduce formulae of Frobenius-Schur indicators of simple objects of Tambara-Yamagami categories. By using techniques of the Fourier transform on finite abelian groups, we study some arithmetic properties of indicators. We also give some applications to Hopf algebras.",

keywords = "Frobenius-Schur indicator, Fusion category, Hopf algebra, Tambara-Yamagami category",

author = "Kenichi Shimizu",

note = "Funding Information: The author is supported by Grant-in-Aid for JSPS Fellows.",

year = "2011",

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Y1 - 2011/4/15

N2 - We introduce formulae of Frobenius-Schur indicators of simple objects of Tambara-Yamagami categories. By using techniques of the Fourier transform on finite abelian groups, we study some arithmetic properties of indicators. We also give some applications to Hopf algebras.

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KW - Hopf algebra

KW - Tambara-Yamagami category

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