# The Ringel dual of the Auslander–Dlab–Ringel algebra

Conde, T
Erdmann, K

15 June 2018

## Journal:

Journal of Algebra

## Last Updated:

2020-10-05T05:32:15.613+01:00

504

## DOI:

10.1016/j.jalgebra.2018.02.029

506-535

## abstract:

© 2018 Elsevier Inc. The ADR algebra RA of a finite-dimensional algebra A is a quasihereditary algebra. In this paper we study the Ringel dual R(RA) of RA. We prove that R(RA) can be identified with (RAop)op, under certain ‘minimal’ regularity conditions for A. In particular, over algebraically closed fields the Ringel dual of the ADR algebra RA is Morita equivalent to (RAop)op (with respect to a canonical labelling) if and only if all projective and injective A-modules are rigid and have the same Loewy length. We also give necessary and sufficient conditions for the ADR algebra to be Ringel selfdual.

829829

Not Submitted

Journal Article