The Ringel dual of the Auslander-Dlab-Ringel algebra
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...
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| Format: | Journal article |
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Elsevier
2018
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| _version_ | 1797055861434089472 |
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| author | Conde, T Erdmann, K |
| author_facet | Conde, T Erdmann, K |
| author_sort | Conde, T |
| collection | OXFORD |
| description | 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 give necessary and sufficient conditions for the ADR algebra to be Ringel selfdual. |
| first_indexed | 2024-03-06T19:15:18Z |
| format | Journal article |
| id | oxford-uuid:1824e171-471c-40dd-8044-b39e3aeba7d4 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:15:18Z |
| publishDate | 2018 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:1824e171-471c-40dd-8044-b39e3aeba7d42022-03-26T10:41:39ZThe Ringel dual of the Auslander-Dlab-Ringel algebraJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1824e171-471c-40dd-8044-b39e3aeba7d4Symplectic Elements at OxfordElsevier2018Conde, TErdmann, KThe 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 give necessary and sufficient conditions for the ADR algebra to be Ringel selfdual. |
| spellingShingle | Conde, T Erdmann, K The Ringel dual of the Auslander-Dlab-Ringel algebra |
| title | The Ringel dual of the Auslander-Dlab-Ringel algebra |
| title_full | The Ringel dual of the Auslander-Dlab-Ringel algebra |
| title_fullStr | The Ringel dual of the Auslander-Dlab-Ringel algebra |
| title_full_unstemmed | The Ringel dual of the Auslander-Dlab-Ringel algebra |
| title_short | The Ringel dual of the Auslander-Dlab-Ringel algebra |
| title_sort | ringel dual of the auslander dlab ringel algebra |
| work_keys_str_mv | AT condet theringeldualoftheauslanderdlabringelalgebra AT erdmannk theringeldualoftheauslanderdlabringelalgebra AT condet ringeldualoftheauslanderdlabringelalgebra AT erdmannk ringeldualoftheauslanderdlabringelalgebra |