On extensions of two families of Tambara–Yamagami categories

Abstract

In this paper, we study the extension of a Tambara–Yamagami category which is of type ${\mathbb{Z}}_p$ or ${\mathbb{Z}}_4,$ where p is a prime number. When the extensions are braided, we further classify the former one in the sense of tensor equivalence and the later one in the sense of Morita equivalence.

Keywords:

• Extension
• fusion category
• group-theoretical fusion category
• Tambara– Yamagami category

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 18D10
• 16T05

Additional information

Funding

The research of the author is partially supported by the Natural Science Foundation of Jiangsu Providence (Grant No. BK20201390) and the startup foundation for introducing talent of NUIST (Grant No. 2018R039).