Non-trivially graded self-dual fusion categories of rank 4 (Q681759)

The paper under review is devoted to classify the Grothendieck ring of self-dual fusion categories of rank \(4\) which admit non-trivial grading. In particular, the authors determine their universal grading groups, fusion rules and Frobenius-Perron dimensions of their simple objects. Moreover, if the fusion category \(\mathcal C\) considered is spherical, they prove that the Grothendieck ring of \(\mathcal C\) is isomorphic to \(Fib\otimes \mathbb{Z}[\mathbb{Z}_2]\), where \(Fib\) is the Fibonacci fusion ring and \(\mathbb{Z}[\mathbb{Z}_2]\) is the group ring on \(\mathbb{Z}_2\).