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Burnside rings for Real 2-representation theory : the linear theory communications
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Rumynin, Dmitriy and Young, Matthew B. (2021) Burnside rings for Real 2-representation theory : the linear theory communications. Communications in Contemporary Mathematics, 23 (5). 2050012. doi:10.1142/S0219199720500121 ISSN 0219-1997.
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Official URL: https://doi.org/10.1142/S0219199720500121
Abstract
This paper is a fundamental study of the Real 2-representation theory of 2-groups. It also contains many new results in the ordinary (non-Real) case. Our framework relies on a 2-equivariant Morita bicategory, where a novel construction of induction is introduced. We identify the Grothendieck ring of Real 2-representations as a Real variant of the Burnside ring of the fundamental group of the 2-group and study the Real categorical character theory. This paper unifies two previous lines of inquiry, the approach to 2-representation theory via Morita theory and Burnside rings, initiated by the first author and Wendland, and the Real 2-representation theory of 2-groups, as studied by the second author.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Categories (Mathematics) , Representations of groups, Burnside rings, Morita duality | ||||||||
| Journal or Publication Title: | Communications in Contemporary Mathematics | ||||||||
| Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||||||
| ISSN: | 0219-1997 | ||||||||
| Official Date: | August 2021 | ||||||||
| Dates: |
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| Volume: | 23 | ||||||||
| Number: | 5 | ||||||||
| Article Number: | 2050012 | ||||||||
| DOI: | 10.1142/S0219199720500121 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | First published in Communications in Contemporary Mathematics in [volume/issue number and year], published by the American Mathematical Society. | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 24 January 2020 | ||||||||
| Date of first compliant Open Access: | 27 February 2021 | ||||||||
| Related URLs: | |||||||||
| Open Access Version: |
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