On an analogue of a Brauer theorem for fusion categories (Q331064)

Let \(G\) be a finite group and \(M\) a faithful complex linear representation of \(G\). The celebrated theorem of Brauer states that any other complex representation of \(G\) can be found as a constituent of at least one tensor power of \(M\). The aim of this paper is to generalize this result to fusion categories. The author realize this aim in the following case: the fusion category \(\mathcal{C}\) with commutative Grothendieck ring \(K_{0}(\mathcal{C})\). As a key contribution of this paper, the author finds a suitable concept of kernel for objects in arbitrary fusion category. The author uses Frobenius-Perron dimension to define this concept. Other invariants such as index and order are also discussed.