A Higher Frobenius–Schur Indicator Formula for Group-Theoretical Fusion Categories
A Higher Frobenius–Schur Indicator Formula for Group-Theoretical Fusion Categories
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群论融合范畴的更高Frobenius-Schur指标公式
DOI：
10.1007/s00220-015-2437-2
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发表时间：
2015
影响因子：
2.4
通讯作者：
P. Schauenburg
中科院分区：
文献类型：
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作者：
P. Schauenburg
群论融合范畴是由有限群及其上同调的数据定义的：有限群G具有一个三上循环ω，子群G具有一个二上链，其上边界是ω的限制。范畴的对象是具有适当扭曲作用的G-分次向量空间;张量积的结合性由ω控制。简单的对象参数化的有限群，即稳定器在H的右H-陪集在G中的投影表示，相对于两个上循环定义的初始数据。我们推导和研究的一般公式，表示更高的Frobenius-Schur指标的简单对象的群论融合范畴的群论和上同调数据定义的类别和描述其simples。
Group-theoretical fusion categories are defined by data concerning finite groups and their cohomology: a finite groupGendowed with a three-cocycleω, and a subgroupendowed with a two-cochain whose coboundary is the restriction ofω. The objects of the category areG-graded vector spaces with suitably twisted-actions; the associativity of tensor products is controlled byω. Simple objects are parametrized in terms of projective representations of finite groups, namely of the stabilizers inHof rightH-cosets inG, with respect to two-cocycles defined by the initial data. We derive and study general formulas that express the higher Frobenius–Schur indicators of simple objects in a group-theoretical fusion category in terms of the group-theoretical and cohomological data defining the category and describing its simples.