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  Braided Picard groups and graded extensions of braided tensor categories

Davydov, A., & Nikshych, D. (2021). Braided Picard groups and graded extensions of braided tensor categories. Selecta Mathematica, 27(4): 65. doi:10.1007/s00029-021-00670-1.

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Item Permalink: https://hdl.handle.net/21.11116/0000-000B-02C6-3 Version Permalink: https://hdl.handle.net/21.11116/0000-000D-F618-3
Genre: Journal Article

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 Creators:
Davydov, Alexei1, Author           
Nikshych, Dmitri, Author
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Quantum Algebra, Category Theory
 Abstract: We classify various types of graded extensions of a finite braided tensor
category $\cal B$ in terms of its $2$-categorical Picard groups. In particular,
we prove that braided extensions of $\cal B$ by a finite group $A$ correspond
to braided monoidal $2$-functors from $A$ to the braided $2$-categorical Picard
group of $\cal B$ (consisting of invertible central $\cal B$-module
categories). Such functors can be expressed in terms of the Eilnberg-Mac~Lane
cohomology. We describe in detail braided $2$-categorical Picard groups of
symmetric fusion categories and of pointed braided fusion categories.

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Language(s): eng - English
 Dates: 2021
 Publication Status: Issued
 Pages: 87
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 2006.08022
DOI: 10.1007/s00029-021-00670-1
 Degree: -

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Title: Selecta Mathematica
Source Genre: Journal
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Publ. Info: Birkhäuser
Pages: - Volume / Issue: 27 (4) Sequence Number: 65 Start / End Page: - Identifier: -