A class of prime fusion categories of dimension 2N.

We study a class of strictly weakly integral fusion categories IN,ζ, where N ≥ 1 is a natural number and ζ is a 2N th root of unity, that we call N-Ising fusion categories. An N-Ising fusion category has Frobenius-Perron dimension 2N+1 and is a graded extension of a pointed fusion category of rank 2 by the cyclic group of order Z2N. 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. [ABSTRACT FROM AUTHOR]