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The singularity and cosingularity categories of C ∗ B G for groups with cyclic Sylow p-subgroups
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Benson, David and Greenlees, John (2023) The singularity and cosingularity categories of C ∗ B G for groups with cyclic Sylow p-subgroups. Algebras and Representation Theory, 26 . pp. 1181-1216. doi:10.1007/s10468-022-10129-2 ISSN 1386-923X.
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Official URL: https://doi.org/10.1007/s10468-022-10129-2
Abstract
We construct a differential graded algebra (DGA) modelling certain A∞ algebras associated with a finite group G with cyclic Sylow subgroups, namely H∗BG and H∗ΩBG∧p. We use our construction to investigate the singularity and cosingularity categories of these algebras. We give a complete classification of the indecomposables in these categories, and describe the Auslander--Reiten quiver. The theory applies to Brauer tree algebras in arbitrary characteristic, and we end with an example in characteristic zero coming from the Hecke algebras of symmetric groups.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Algebras and Representation Theory | ||||||||
Publisher: | Springer Netherlands | ||||||||
ISSN: | 1386-923X | ||||||||
Official Date: | August 2023 | ||||||||
Dates: |
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Volume: | 26 | ||||||||
Number of Pages: | 36 | ||||||||
Page Range: | pp. 1181-1216 | ||||||||
DOI: | 10.1007/s10468-022-10129-2 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 12 April 2022 | ||||||||
Date of first compliant Open Access: | 16 May 2022 | ||||||||
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