Extensions of a near-group category of type (Z2,1)

We study the G -extensions C of a near-group fusion category of type ( Z 2 , 1 ) . If C is braided we prove that C can be reconstructed from pointed fusion categories by Z 2 -extensions or Z 2 -equivariantizations. Furthermore, if C is also integral, or C is equivalent as a tensor category to the ca...

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Bibliographic Details
Published in:Acta mathematica Hungarica 2022, Vol.167 (2), p.404-418
Main Author: Dai, L.
Format: Article
Language:English
Subjects:
Algebra
Categories
Equivalence
Mathematics
Mathematics and Statistics
Tensors
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Summary:We study the G -extensions C of a near-group fusion category of type ( Z 2 , 1 ) . If C is braided we prove that C can be reconstructed from pointed fusion categories by Z 2 -extensions or Z 2 -equivariantizations. Furthermore, if C is also integral, or C is equivalent as a tensor category to the category of finite dimensional representations of a semisimple Hopf algebra, we prove that C is group-theoretical, which completes the classification of these categories in the sense of Morita equivalence.
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-022-01256-9