The Singularity and Cosingularity Categories of C ∗ B G for Groups with Cyclic Sylow p-subgroups

David Benson* (Corresponding Author), John Greenlees

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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∗BG∧
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.
Original languageEnglish
JournalAlgebras and Representation Theory
Early online date14 May 2022
DOIs
Publication statusE-pub ahead of print - 14 May 2022

Keywords

  • A∞ algebras
  • Auslander–Reiten quiver
  • Auslander–Reiten triangles
  • Brauer trees
  • Cyclic Sylow subgroups
  • Cohomology of groups
  • Cosingularity categories
  • Derived categories
  • DG Hopf algebras
  • Hecke algebras
  • Hochschild cohomology
  • Loop spaces
  • Massey products
  • p-completed classifying spaces ·
  • Singularity categories
  • Spectral sequences

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