Ringel duality and Auslander-Dlab-Ringel algebras
Representation Theory
2018-10-09 v2 Rings and Algebras
Abstract
We introduce a new class of quasi-hereditary algebras, containing in particular the Auslander-Dlab-Ringel (ADR) algebras. We show that this new class of algebras is preserved under Ringel duality, which determines in particular explicitly the Ringel dual of any ADR algebra. As a special case of our theory, it follows that, under very restrictive conditions, an ADR algebra is Ringel dual to another one. The latter provides an alternative proof for a recent result of Conde and Erdmann, and places it in a more general setting.
Cite
@article{arxiv.1710.08019,
title = {Ringel duality and Auslander-Dlab-Ringel algebras},
author = {Kevin Coulembier},
journal= {arXiv preprint arXiv:1710.08019},
year = {2018}
}