On Integral Fusion Categories with Low-Dimensional Simple Objects

Abstract

Let k be an algebraically closed field of characteristic zero. In this article, we consider an integral fusion category over k in which the Frobenius–Perron dimensions of its simple objects are at most 3. We prove that such fusion category is of Frobenius type. In addition, we also prove that such fusion category is not simple.

Key Words:

• Frobenius property
• Frobenius–Perron dimension
• Fusion category

2010 Mathematics Subject Classification:

• 18D10
• 16T05

Notes

Communicated by V. A. Artamonov.