On higher Frobenius-Schur indicators

Yevgenia Kashina; Yorck Sommerhäuser; Yongchang Zhu

doi:10.1090/memo/0855

On higher Frobenius-Schur indicators

Yevgenia Kashina^*, Yorck Sommerhäuser, Yongchang Zhu

^*Corresponding author for this work

Research output: Contribution to journal › Review article › peer-review

81 Citations (Scopus)

Abstract

We study the higher Frobenius-Schur indicators of modules over semisimple Hopf algebras, and relate them to other invariants as the exponent, the order, and the index. We prove various divisibility and integrality results for these invariants. In particular, we prove a version of Cauchy's theorem for semisimple Hopf algebras. Furthermore, we give some examples that illustrate the general theory.

Original language	English
Pages (from-to)	1-71
Number of pages	71
Journal	Memoirs of the American Mathematical Society
Volume	181
Issue number	855
DOIs	https://doi.org/10.1090/memo/0855
Publication status	Published - May 2006
Externally published	Yes

Keywords

Cauchy's theorem
Character
Exponent
Index
Order
Perron-Frobenius theorem
Semisimple Hopf algebra
Sweedler power

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10.1090/memo/0855

Cite this

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abstract = "We study the higher Frobenius-Schur indicators of modules over semisimple Hopf algebras, and relate them to other invariants as the exponent, the order, and the index. We prove various divisibility and integrality results for these invariants. In particular, we prove a version of Cauchy's theorem for semisimple Hopf algebras. Furthermore, we give some examples that illustrate the general theory.",

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author = "Yevgenia Kashina and Yorck Sommerh{\"a}user and Yongchang Zhu",

year = "2006",

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T1 - On higher Frobenius-Schur indicators

AU - Kashina, Yevgenia

AU - Sommerhäuser, Yorck

AU - Zhu, Yongchang

PY - 2006/5

Y1 - 2006/5

N2 - We study the higher Frobenius-Schur indicators of modules over semisimple Hopf algebras, and relate them to other invariants as the exponent, the order, and the index. We prove various divisibility and integrality results for these invariants. In particular, we prove a version of Cauchy's theorem for semisimple Hopf algebras. Furthermore, we give some examples that illustrate the general theory.

AB - We study the higher Frobenius-Schur indicators of modules over semisimple Hopf algebras, and relate them to other invariants as the exponent, the order, and the index. We prove various divisibility and integrality results for these invariants. In particular, we prove a version of Cauchy's theorem for semisimple Hopf algebras. Furthermore, we give some examples that illustrate the general theory.

KW - Cauchy's theorem

KW - Character

KW - Exponent

KW - Index

KW - Order

KW - Perron-Frobenius theorem

KW - Semisimple Hopf algebra

KW - Sweedler power

UR - https://openalex.org/W2104893011

UR - https://www.scopus.com/pages/publications/33646432201

U2 - 10.1090/memo/0855

DO - 10.1090/memo/0855

M3 - Review article

SN - 0065-9266

VL - 181

SP - 1

EP - 71

JO - Memoirs of the American Mathematical Society

JF - Memoirs of the American Mathematical Society

IS - 855

ER -

On higher Frobenius-Schur indicators

Abstract

Keywords

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