New York Journal of Mathematics
Volume 27 (2021), 141-163


Jingcheng Dong, Sonia Natale, and Hua Sun

A class of prime fusion categories of dimension 2N

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Published: January 4, 2021.
Keywords: Fusion category; braided fusion category; group extension; Ising category.
Subject: 18M20.

We study a class of strictly weakly integral fusion categories IN, ζ, where N≥1 is a natural number and ζ is a 2Nth 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.


J. Dong is partially supported by the Natural Science Foundation of Jiangsu Providence (Grant No. BK20201390), the startup foundation for introducing talent of NUIST (Grant No. 2018R039), and the Natural Science Foundation of China (Grant No. 11201231). S. Natale is partially supported by CONICET and Secyt-UNC. The work of S. Natale was done in part during visits to NUIST in Nanjing, and ECNU in Shanghai; she thanks both mathematics departments for the outstanding hospitality.

Author information

Jingcheng Dong:
College of Mathematics and Statistics
Nanjing University of Information Science and Technology
Nanjing 210044, China


Sonia Natale:
Facultad de Matemática, Astronomía, Física y Computación
Universidad Nacional de Córdoba
CIEM -- CONICET, (5000) Ciudad Universitaria, Córdoba, Argentina


Hua Sun:
Department of Mathematics
Yangzhou University
Yangzhou, Jiangsu 225002, China