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2-groups, 2-characters, and Burnside rings
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Rumynin, Dmitriy and Wendland, Alex (2018) 2-groups, 2-characters, and Burnside rings. Advances in Mathematics, 338 . pp. 196-236. doi:10.1016/j.aim.2018.09.003 ISSN 0001-8708.
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Official URL: https://doi.org/10.1016/j.aim.2018.09.003
Abstract
We study 2-representations, i.e., actions of 2-groups on 2-vector spaces. Our main focus is character theory for 2-representations. To this end we employ the technique of extended Burnside rings. Our main theorem is that the Ganter–Kapranov 2-character is a particular mark homomorphism of the Burnside ring. As an application we give a new proof of Osorno's formula for the Ganter–Kapranov 2-character of a finite group.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
Library of Congress Subject Headings (LCSH): | Burnside rings, Vector spaces | |||||||||
Journal or Publication Title: | Advances in Mathematics | |||||||||
Publisher: | Academic Press | |||||||||
ISSN: | 0001-8708 | |||||||||
Official Date: | 7 November 2018 | |||||||||
Dates: |
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Volume: | 338 | |||||||||
Page Range: | pp. 196-236 | |||||||||
DOI: | 10.1016/j.aim.2018.09.003 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Date of first compliant deposit: | 29 August 2018 | |||||||||
Date of first compliant Open Access: | 10 September 2019 | |||||||||
RIOXX Funder/Project Grant: |
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