In this paper, we consider fusion categories generated by a self-dual simple object of FP-dimension 2. We use the classification results of indecomposable generalized Cartan matrices to determine possible types of these fusion categories. It turns out that there are only five types for such categories. Moreover, the fusion rules of all types of these fusion categories are explicitly described according to their valued graphs. This gives a classification of these fusion categories up to Grothendieck equivalence.

中文翻译：

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FP-dimension 2的自对偶简单对象生成的融合类别分类

在本文中，我们考虑由 FP 维 2 的自对偶简单对象生成的融合类别。我们使用不可分解的广义 Cartan 矩阵的分类结果来确定这些融合类别的可能类型。事实证明，此类类别只有五种类型。此外，这些融合类别的所有类型的融合规则都根据它们的值图进行了明确的描述。这给出了这些融合类别的分类，直至 Grothendieck 等价。