Cyclic extensions of fusion categories via the Brauer-Picard groupoid

  title={Cyclic extensions of fusion categories via the Brauer-Picard groupoid},
  author={Pinhas Grossman and David A. Jordan and Noah Snyder},
  journal={Quantum Topology},
We construct a long exact sequence computing the obstruction space, pi_1(BrPic(C_0)), to G-graded extensions of a fusion category C_0. The other terms in the sequence can be computed directly from the fusion ring of C_0. We apply our result to several examples coming from small index subfactors, thereby constructing several new fusion categories as G-extensions. The most striking of these is a Z/2Z-extension of one of the Asaeda-Haagerup fusion categories, which is one of only two known 3… 
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