# A class of prime fusion categories of dimension $2^N$

@article{Dong2019ACO, title={A class of prime fusion categories of dimension \$2^N\$}, author={Jingcheng Dong and Sonia Natale and Hua Sun}, journal={arXiv: Quantum Algebra}, year={2019} }

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 $2^N$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 $\mathbb Z_{2^N}$. We show that every braided $N$-Ising fusion category is prime and also that there exists a slightly…

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