## 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.

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 language | English |
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Journal | Algebras and Representation Theory |

Early online date | 14 May 2022 |

DOIs | |

Publication status | E-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