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A class of prime fusion categories of dimension $2^N$ (1910.07034v2)

Published 15 Oct 2019 in math.QA

Abstract: We study a class of strictly weakly integral fusion categories $\mathfrak{I}{N, \zeta}$, where $N \geq 1$ is a natural number and $\zeta$ is a $2N$th root of unity, that we call $N$-Ising fusion categories. An $N$-Ising fusion category has Frobenius-Perron dimension $2{N+1}$ and is a graded extension of a pointed fusion category of rank 2 by the cyclic group of order $\mathbb Z{2N}$. We show that every braided $N$-Ising fusion category is prime and also that there exists a slightly degenerate $N$-Ising braided fusion category for all $N > 2$. We also prove a structure result for braided extensions of a rank 2 pointed fusion category in terms of braided $N$-Ising fusion categories.

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