Classification of Super-Modular Categories by Rank
Classification of Super-Modular Categories by Rank
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DOI：
10.1007/s10468-019-09873-9
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发表时间：
2017-05
影响因子：
0.6
通讯作者：
P. Bruillard;César Galindo;S. Ng;J. Plavnik;E. Rowell;Zhenghan Wang
中科院分区：
文献类型：
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作者：
P. Bruillard;César Galindo;S. Ng;J. Plavnik;E. Rowell;Zhenghan Wang
我们追求一个分类的低秩超模范畴平行的模块范畴。我们对rank = 6以下的所有超模范畴进行分类，并对rank = 11以下的自旋模范畴进行分类。特别地，我们证明了在fusion规则下，秩为2，4，6的非分裂超模范畴PSU（2）4k+ 2fork= 0，1，2是唯一的.通过将众所周知的约束从模块类别调整和扩展到超模块类别（例如Verlinde和Frobenius-Schur指标公式），可以促进这种分类。
We pursue a classification of low-rank super-modular categories parallel to that of modular categories. We classify all super-modular categories up to rank = 6, and spin modular categories up to rank = 11. In particular, we show that, up to fusion rules, there is exactly one non-split super-modular category of rank 2, 4 and 6, namelyPSU(2)4k+ 2fork= 0,1 and 2. This classification is facilitated by adapting and extending well-known constraints from modular categories to super-modular categories, such as Verlinde and Frobenius-Schur indicator formulae.