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ISSN 1947-6221(e) ISSN 0065-9266(p)

Hopf algebras and congruence subgroups

Authors: Yorck Sommerhäuser and Yongchang Zhu
Journal: Memoirs of the AMS
MSC (2010): Primary 16T05; Secondary 17B37
Posted: February 7, 2012
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Abstract: 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.

References

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