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

Abstract

We construct a differential graded algebra (DGA) modelling certain $A_{\infty }$ A ∞ algebras associated with a finite group G with cyclic Sylow subgroups, namely H∗BG and $H_{*}{\Omega } BG{^{^{\wedge }}_p}$ H ∗ Ω B G 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.