Classification of fusion categories generated by a self-dual simple object of FP-dimension 2
Classification of fusion categories generated by a self-dual simple object of FP-dimension 2
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FP 维 2 的自对偶简单对象生成的融合类别的分类
DOI：
10.1142/s0219498822500748
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发表时间：
2020-12
期刊：
影响因子：
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通讯作者：
Libin Li
中科院分区：
文献类型：
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作者：
Zhihua Wang;Jingcheng Dong;Libin Li
在本文中，我们考虑融合范畴产生的自对偶简单对象的FP-维2。我们使用不可分解的广义Cartan矩阵的分类结果，以确定这些融合类别的可能类型。事实证明，这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显式描述根据其值图。这给出了一个分类的这些融合类别高达Grothendieck等价。
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.