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

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• 作者：Peter Schauenburg
• 刊名：Communications in Mathematical Physics
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：340
• 期：2
• 页码：833-849
• 全文大小：481 KB
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• 作者单位：Peter Schauenburg (1)
  
  1. Institut de Mathématiques de Bourgogne, UMR 5584 CNRS, Université Bourgogne Franche-Comté, 21000, Dijon, France
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Quantum Physics
  Quantum Computing, Information and Physics
  Complexity
  Statistical Physics
  Relativity and Cosmology
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0916

文摘

Group-theoretical fusion categories are defined by data concerning finite groups and their cohomology: a finite group G endowed with a three-cocycle ω, and a subgroup \({H\subset G}\) endowed with a two-cochain whose coboundary is the restriction of ω. The objects of the category are G-graded vector spaces with suitably twisted \({H}\)-actions; the associativity of tensor products is controlled by ω. 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. Communicated by Y. KawahigashiResearch partially supported through a FABER Grant by the Conseil régional de Bourgogne.