Fusion Subcategories of Representation Categories of Twisted Quantum Doubles of Finite Groups

Deepak Naidu1 Dmitri Nikshych2 and Sarah Witherspoon3

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Fusion Subcategories of Representation Categories of Twisted Quantum Doubles of Finite Groups

机译：有限群的扭曲量子对偶的表示类别的融合子类别

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We describe all fusion subcategories of the representation category of a twisted quantum double , where G is a finite group and is a 3-cocycle on G. In view of the fact that every group-theoretical braided fusion category can be embedded into some , this gives a complete description of all group-theoretical braided fusion categories. We describe the lattice and give formulas for some invariants of the fusion subcategories of . We also give a characterization of group-theoretical braided fusion categories as equivariantizations of pointed categories.

机译：我们描述了一个扭曲的量子对偶表示类别的所有融合子类别，其中G是一个有限群，是G上的一个3环。鉴于每个群理论编织的聚变类别都可以嵌入到其中，给出了所有基于群论的编织融合类别的完整描述。我们描述的格并给出了融合子类的一些不变量的公式。我们还将群体理论的编织融合类别的特征描述为针对类别的等变。

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《International Mathematics Research Notices》 |2009年第22期|p.4183-4219|共37页
作者
Deepak Naidu1 Dmitri Nikshych2 and Sarah Witherspoon3;
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1Department of Mathematics, Texas A&

M University, College Station, TX 77843, USA 2Department of Mathematics and Statistics, University of New Hampshire, Durham, NH 03824, USA 3Department of Mathematics, Texas A&

M University, College Station, TX 77843, USA;

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Fusion Subcategories of Representation Categories of Twisted Quantum Doubles of Finite Groups

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