The Ringel dual of the Auslander–Dlab–Ringel algebra

Author: 

Conde, T
Erdmann, K

Publication Date: 

15 June 2018

Journal: 

Journal of Algebra

Last Updated: 

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

Volume: 

504

DOI: 

10.1016/j.jalgebra.2018.02.029

page: 

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.

Symplectic id: 

829829

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article