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The Ringel dual of the Auslander-Dlab-Ringel algebra

Abstract:

The ADR algebra RAof a finite-dimensional algebra Ais 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 RAis 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...

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Publication status:
In press
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.jalgebra.2018.02.029

Authors

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Computer Science; Mathematical Institute
Oxford college:
Somerville College
Role:
Author
Publisher:
Elsevier
Journal:
Journal of Algebra More from this journal
Volume:
504
Pages:
506-535
Publication date:
2018-03-07
Acceptance date:
2018-02-28
DOI:
ISSN:
0021-8693
Keywords:
Pubs id:
pubs:846078
UUID:
uuid:1824e171-471c-40dd-8044-b39e3aeba7d4
Local pid:
pubs:846078
Source identifiers:
846078
Deposit date:
2018-05-04

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