On the graded center of graded categories

On the graded center of graded categories

We study the G-centers of G-graded monoidal categories where G is an arbitrary group. We prove that for any spherical G-fusion category C over an algebraically closed field such that the dimension of the neutral component of C is non-zero, the G-center of C is a G-modular category. This generalizes...

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Veröffentlicht in:Journal of pure and applied algebra 2013-10, Vol.217 (10), p.1895-1941
Hauptverfasser: Turaev, Vladimir, Virelizier, Alexis
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Quantum Algebra
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Zusammenfassung:We study the G-centers of G-graded monoidal categories where G is an arbitrary group. We prove that for any spherical G-fusion category C over an algebraically closed field such that the dimension of the neutral component of C is non-zero, the G-center of C is a G-modular category. This generalizes a theorem of M. Müger corresponding to G=1. We also exhibit interesting objects of the G-center.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2013.01.011