A Higher Frobenius-Schur Indicator Formula for Group-Theoretical Fusion Categories

被引:3
作者
Schauenburg, Peter [1 ]
机构
[1] Univ Bourgogne Franche Comte, CNRS, Inst Math Bourgogne, UMR 5584, F-21000 Dijon, France
关键词
CENTRAL INVARIANTS; EQUIVALENCE;
D O I
10.1007/s00220-015-2437-2
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Group-theoretical fusion categories are defined by data concerning finite groups and their cohomology: a finite group G endowed with a three-cocycle omega, and a subgroup endowed with a two-cochain whose coboundary is the restriction of omega. The objects of the category are G-graded vector spaces with suitably twisted -actions; the associativity of tensor products is controlled by omega. Simple objects are parametrized in terms of projective representations of finite groups, namely of the stabilizers in H of right H-cosets in G, 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.
引用
收藏
页码:833 / 849
页数:17
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