• Corpus ID: 204734125

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}
}

• Jingcheng Dong, S. Natale, Hua Sun
• Published 15 October 2019
• Mathematics
• arXiv: Quantum Algebra

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 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.