Book's by Yongchang Zhu

Hopf Algebras and Congruence Subgroups

By: Yorck Sommerhäuser, Yongchang Zhu

Hopf Algebras and Congruence Subgroups

By: Yorck Sommerhäuser, Yongchang Zhu

On Higher Frobenius-Schur Indicators

By: Yevgenia Kashina, Yorck Sommerhäuser, Yongchang Zhu

On Higher Frobenius-Schur Indicators

By: Yevgenia Kashina,Yorck Sommerhäuser,Yongchang Zhu

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On Higher Frobenius-Schur Indicators

By: Yevgenia Kashina,Yorck Sommerhäuser,Yongchang Zhu

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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Page Count

82

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821838865

ISBN 13

9780821838860

Hopf Algebras and Congruence Subgroups

By: Yorck Sommerhäuser,Yongchang Zhu

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Hopf Algebras and Congruence Subgroups

By: Yorck Sommerhäuser,Yongchang Zhu

We prove that the kernel of the action of the modular group on the center of a semisimple factorizable Hopf algebra is a congruence subgroup whenever this action is linear. If the action is only projective, we show that the projective kernel is a congruence subgroup. To do this, we introduce a class of generalized Frobenius-Schur indicators and endow it with an action of the modular group that is compatible with the original one.

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Page Count

146

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821869132

ISBN 13

9780821869130

Hopf Algebras and Congruence Subgroups

By: Yorck Sommerhäuser,Yongchang Zhu

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Hopf Algebras and Congruence Subgroups

By: Yorck Sommerhäuser,Yongchang Zhu

We prove that the kernel of the action of the modular group on the center of a semisimple factorizable Hopf algebra is a congruence subgroup whenever this action is linear. If the action is only projective, we show that the projective kernel is a congruence subgroup. To do this, we introduce a class of generalized Frobenius-Schur indicators and endow it with an action of the modular group that is compatible with the original one.

Average ratings

N/A

5

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4

0%

3

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2

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1

0%

Age

Page Count

146

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821869132

ISBN 13

9780821869130

On Higher Frobenius-Schur Indicators

By: Yevgenia Kashina,Yorck Sommerhäuser,Yongchang Zhu

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On Higher Frobenius-Schur Indicators

By: Yevgenia Kashina,Yorck Sommerhäuser,Yongchang Zhu

Studies the higher Frobenius-Schur indicators of modules over semisimple Hopf algebras, and relates them to other invariants as the exponent, the order, and the index. This title intends to prove various divisibility and integrality results for these invariants as well as a version of Cauchy's theorem for semisimple Hopf algebras.

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