Non-trivially Graded Self-dual Fusion Categories of Rank 4  

作　　者：Jing Cheng DONG Liang Yun ZHANG Li DAI 

机构地区：[1]College of Engineering, Nanjing Agricultural University, Nanjing 210031, P. R. China [2]College of Science, Nanjing Agricultural University, Nanjing 210095, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2018年第2期275-287,共13页数学学报（英文版）

基　　金：Supported by the Fundamental Research Funds for the Central Universities(Grant No.KYZ201564);the Natural Science Foundation of China(Grant Nos.11571173,11201231);the Qing Lan Project

摘　　要：Let C be a self-dual spherical fusion categories of rank 4 with non-trivial grading. We complete the classification of Grothendieck ring K（C） of C; that is, we prove that K（C） = Fib Z[Z2], where Fib is the Fibonacci fusion ring and Z[Z2] is the group ring on Z2. In particular, if C is braided, then it is equivalent to Fib Vecwz2 as fusion categories, where Fib is a Fibonacci category and Vecwz2 is a rank 2 pointed fusion category.Let C be a self-dual spherical fusion categories of rank 4 with non-trivial grading. We complete the classification of Grothendieck ring K（C） of C; that is, we prove that K（C） = Fib Z[Z2], where Fib is the Fibonacci fusion ring and Z[Z2] is the group ring on Z2. In particular, if C is braided, then it is equivalent to Fib Vecwz2 as fusion categories, where Fib is a Fibonacci category and Vecwz2 is a rank 2 pointed fusion category.

关 键 词：Fusion categories universal grading small rank Frobenius-Perron dimension 

分 类 号：O1[理学—数学]