 

Jingcheng Dong,
Sonia Natale, and
Hua Sun
A class of prime fusion categories of dimension 2^{N}
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Published: 
January 4, 2021. 
Keywords: 
Fusion category; braided fusion category; group extension; Ising category. 
Subject: 
18M20. 


Abstract
We study a class of strictly weakly integral fusion categories I_{N, ζ}, where N≥1 is a natural number and ζ is a 2^{N}th root of unity, that we call NIsing fusion categories. An NIsing fusion category has FrobeniusPerron dimension 2^{N+1} and is a graded extension of a pointed fusion category of rank 2 by the cyclic group of order Z_{2N}. We show that every braided NIsing fusion category is prime and also that there exists a slightly degenerate NIsing 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 NIsing fusion categories. 

Acknowledgements
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 SecytUNC. 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
jcdong@nuist.edu.cn
Sonia Natale:
Facultad de Matemática, Astronomía, Física y Computación
Universidad Nacional de Córdoba
CIEM  CONICET, (5000) Ciudad Universitaria, Córdoba, Argentina
natale@famaf.unc.edu.ar
Hua Sun:
Department of Mathematics
Yangzhou University
Yangzhou, Jiangsu 225002, China
d160028@yzu.edu.cn

