Modular categories of dimension $p^3m$ with $m$ square-free
Modular categories of dimension $p^3m$ with $m$ square-free
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DOI：
10.1090/proc/13776
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发表时间：
2016-09
影响因子：
1
通讯作者：
P. Bruillard;J. Plavnik;E. Rowell
中科院分区：
文献类型：
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作者：
P. Bruillard;J. Plavnik;E. Rowell
给出了维为$p^3m$的模范畴的一个完全分类，其中$p$为素数，$m$为无平方整数。当$p$是奇数时，所有这些类别都是指向的。对于$p=2$，在某些单位根处遇到与正交量子群具有相同融合环的模范畴，即$SO(2m)_2$。作为直接步骤，我们分类了一类更一般的所谓偶次亚普勒模范畴，它们具有与$SO(2N)_2$和$N$奇数相同的融合规则。
We give a complete classification of modular categories of dimension $p^3m$ where $p$ is prime and $m$ is a square-free integer. When $p$ is odd, all such categories are pointed. For $p=2$ one encounters modular categories with the same fusion ring as orthogonal quantum groups at certain roots of unity, namely $SO(2m)_2$. As an immediate step we classify a more general class of so-called even metaplectic modular categories with the same fusion rules as $SO(2N)_2$ with $N$ odd.