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2009 Centers of graded fusion categories
Shlomo Gelaki, Deepak Naidu, Dmitri Nikshych
Algebra Number Theory 3(8): 959-990 (2009). DOI: 10.2140/ant.2009.3.959


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 ZD(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 the existence of zeroes in S-matrices of weakly integral modular categories.


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Shlomo Gelaki. Deepak Naidu. Dmitri Nikshych. "Centers of graded fusion categories." Algebra Number Theory 3 (8) 959 - 990, 2009.


Received: 21 May 2009; Revised: 31 August 2009; Accepted: 9 November 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1201.18006
MathSciNet: MR2587410
Digital Object Identifier: 10.2140/ant.2009.3.959

Primary: 16W30
Secondary: 18D10

Keywords: braided categories , fusion categories , graded tensor categories

Rights: Copyright © 2009 Mathematical Sciences Publishers


Vol.3 • No. 8 • 2009
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