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Centers of graded fusion categories

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arxiv 0905.3117 v1 pith:PKLMEEKM submitted 2009-05-19 math.QA

Shlomo Gelaki , Deepak Naidu , Dmitri Nikshych This is my paper · ORCID
classification math.QA
keywords categoriesfusioncentercentersgradedmodularresulttambara-yamagami
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Let C be a fusion category faithfully graded by a finite group G and let D be the trivial component of this grading. The center Z(C) of C is shown to be canonically equivalent to a G-equivariantization of the relative center Z_D(C). We use this result to obtain a criterion for C to be group-theoretical and apply it to Tambara-Yamagami fusion categories. We also find several new series of modular categories by analyzing the centers of Tambara-Yamagami categories. Finally, we prove a general result about existence of zeroes in S-matrices of weakly integral modular categories.

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Cited by 7 Pith papers

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