# Cyclic extensions of fusion categories via the Brauer-Picard groupoid

@article{Grossman2015CyclicEO, title={Cyclic extensions of fusion categories via the Brauer-Picard groupoid}, author={Pinhas Grossman and David A. Jordan and Noah Snyder}, journal={Quantum Topology}, year={2015}, volume={6}, pages={313-331} }

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…

## 17 Citations

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