Irreducible {\mathbb{Z}}_{+}-modules of near-group fusion ring K({\mathbb{Z}}_{\mathrm{3}}, 3)

Abstract

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

Key words： irreducible {\mathbb{Z}}_{+}-module, near group ring, fusion ring

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