Gentle \(m\)-Calabi-Yau tilted algebras
We prove that all gentle 2-Calabi-Yau tilted algebras are Jacobian, moreover their bound quiver can be obtained via block decomposition. For two related families, the \(m\)-cluster-tilted algebras of type \(\mathbb{A}\) and \(\tilde{\mathbb{A}}\), we prove that a module \(M\) is stable Cohen-Macaula...
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| Date: | 2020 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2020
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1423 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543133795352576 |
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| author | Garcia Elsener, A. |
| author_facet | Garcia Elsener, A. |
| author_sort | Garcia Elsener, A. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2021-01-05T07:08:40Z |
| description | We prove that all gentle 2-Calabi-Yau tilted algebras are Jacobian, moreover their bound quiver can be obtained via block decomposition. For two related families, the \(m\)-cluster-tilted algebras of type \(\mathbb{A}\) and \(\tilde{\mathbb{A}}\), we prove that a module \(M\) is stable Cohen-Macaulay if and only if \(\Omega^{m+1} \tau M \simeq M\). |
| first_indexed | 2026-02-08T07:57:40Z |
| format | Article |
| id | admjournalluguniveduua-article-1423 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:57:40Z |
| publishDate | 2020 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-14232021-01-05T07:08:40Z Gentle \(m\)-Calabi-Yau tilted algebras Garcia Elsener, A. 2-Calabi-Yau tilted algebras, Jacobian algebras, Gentle algebras, derived category, Cohen-Macaulay modules, cluster-tilted algebras 16G20 We prove that all gentle 2-Calabi-Yau tilted algebras are Jacobian, moreover their bound quiver can be obtained via block decomposition. For two related families, the \(m\)-cluster-tilted algebras of type \(\mathbb{A}\) and \(\tilde{\mathbb{A}}\), we prove that a module \(M\) is stable Cohen-Macaulay if and only if \(\Omega^{m+1} \tau M \simeq M\). Lugansk National Taras Shevchenko University CONICET and PICT 2013-0799 ANPCyT 2020-12-30 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1423 10.12958/adm1423 Algebra and Discrete Mathematics; Vol 30, No 1 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1423/pdf Copyright (c) 2020 Algebra and Discrete Mathematics |
| spellingShingle | 2-Calabi-Yau tilted algebras Jacobian algebras Gentle algebras derived category Cohen-Macaulay modules cluster-tilted algebras 16G20 Garcia Elsener, A. Gentle \(m\)-Calabi-Yau tilted algebras |
| title | Gentle \(m\)-Calabi-Yau tilted algebras |
| title_full | Gentle \(m\)-Calabi-Yau tilted algebras |
| title_fullStr | Gentle \(m\)-Calabi-Yau tilted algebras |
| title_full_unstemmed | Gentle \(m\)-Calabi-Yau tilted algebras |
| title_short | Gentle \(m\)-Calabi-Yau tilted algebras |
| title_sort | gentle \(m\)-calabi-yau tilted algebras |
| topic | 2-Calabi-Yau tilted algebras Jacobian algebras Gentle algebras derived category Cohen-Macaulay modules cluster-tilted algebras 16G20 |
| topic_facet | 2-Calabi-Yau tilted algebras Jacobian algebras Gentle algebras derived category Cohen-Macaulay modules cluster-tilted algebras 16G20 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1423 |
| work_keys_str_mv | AT garciaelsenera gentlemcalabiyautiltedalgebras |