Centers of graded fusion categories

Details Centers of graded fusion categories Centers of graded fusion categories

2009-05-19

arxiv.org/abs/0905.3117v1

Algebra Number Theory 3 (2009), no. 8, 959-990

Mathematics

Quantum Algebra

27 pages

Scientific paper

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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