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 ∞ 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.