Irreducible ℤ+-modules of near-group fusion ring K(ℤ3, 3)

The near-group rings are an important class of fusion rings in the theory of tensor categories. In this paper, the irreducible ℤ+-modules over the near-group fusion ring K(ℤ3, 3) are explicitly classified. It turns out that there are only four inequivalent irreducible ℤ+-modules of rank 2 and two inequivalent irreducible ℤ+-modules of rank 4 over K(ℤ3, 3).