Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Centers of graded fusion categories   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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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: atom-ph