Centers of graded fusion categories

By Shlomo Gelaki, D. Venku Naidu, D. Nikshych. 2009

191 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7ba4a749de5fcf086d4906a7e9747c8466a689ec

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Citations in the corpus

On finite-dimensional Hopf algebras (2014, background): “if and only if it is cosemisimple (that is, H∗ is semisimple). ⋄ Given an extension C → K → H → L → C, H is semisimple iﬀ K and L are. Notice that there are semisimple extensions that are not abelian [40, 69, 74]. ⋄ If H is semisimple, then so are HF and Hσ, for any twist F and cocycle σ. If G is a ”
A Finiteness Property for Braided Fusion Categories (2009, methodology): “There are two main sources of weakly integral braided fusion categories in the literature: Drinfeld centers of Tambara-Yamagami categories DT Y(A, χ, τ) (see [19, 17 ] and Section 5 below), and quantum group type modular categories C(soN, q, l) where l = N or 2N if N is even or odd respectively (se”
Anyon condensation and tensor categories (2013, methodology): “his work can also be applied to the condensations in a symmetry enriched topological orders [HW] with small variations. In this case, we must work with algebras in G-crossed braided tensor categories [GNN]. We will give more details elsewhere. A Appendix For the convenience of physics readers, we in”
Fusion categories and homotopy theory (2009, unknown): “The following definition was given in [18].”