On the mutation loops of valued quivers
A mutation loop of a valued quiver, \(Q\), is a combination of quiver automorphisms and mutations that sends \(Q\) to itself. Moreover, it will be called symmetric if it sends \(Q\) to \(\epsilon\sigma(Q)\), \(\epsilon \in \{-1, 1\}\) for some permutation \(\sigma\). A global mutation loop of \(Q\)...
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| Дата: | 2023 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2023
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2083 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-20832023-12-11T16:21:07Z On the mutation loops of valued quivers Saleh, I. cluster algebras, global mutation loops Primary 13F60, Secondary 05E15 A mutation loop of a valued quiver, \(Q\), is a combination of quiver automorphisms and mutations that sends \(Q\) to itself. Moreover, it will be called symmetric if it sends \(Q\) to \(\epsilon\sigma(Q)\), \(\epsilon \in \{-1, 1\}\) for some permutation \(\sigma\). A global mutation loop of \(Q\) is a mutation loop that is symmetric for every quiver in the mutation class of \(Q\). This class of relations contains all the relations of the global mutations group yield from the group action on the mutation class of \(Q\). We identify which quivers have global mutation loops and provide some of them for each case. Lugansk National Taras Shevchenko University University of Wisconsin Whitewater 2023-12-11 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2083 10.12958/adm2083 Algebra and Discrete Mathematics; Vol 36, No 1 (2023) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2083/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2083/1070 Copyright (c) 2023 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
cluster algebras global mutation loops Primary 13F60 Secondary 05E15 |
| spellingShingle |
cluster algebras global mutation loops Primary 13F60 Secondary 05E15 Saleh, I. On the mutation loops of valued quivers |
| topic_facet |
cluster algebras global mutation loops Primary 13F60 Secondary 05E15 |
| format |
Article |
| author |
Saleh, I. |
| author_facet |
Saleh, I. |
| author_sort |
Saleh, I. |
| title |
On the mutation loops of valued quivers |
| title_short |
On the mutation loops of valued quivers |
| title_full |
On the mutation loops of valued quivers |
| title_fullStr |
On the mutation loops of valued quivers |
| title_full_unstemmed |
On the mutation loops of valued quivers |
| title_sort |
on the mutation loops of valued quivers |
| description |
A mutation loop of a valued quiver, \(Q\), is a combination of quiver automorphisms and mutations that sends \(Q\) to itself. Moreover, it will be called symmetric if it sends \(Q\) to \(\epsilon\sigma(Q)\), \(\epsilon \in \{-1, 1\}\) for some permutation \(\sigma\). A global mutation loop of \(Q\) is a mutation loop that is symmetric for every quiver in the mutation class of \(Q\). This class of relations contains all the relations of the global mutations group yield from the group action on the mutation class of \(Q\). We identify which quivers have global mutation loops and provide some of them for each case. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2023 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2083 |
| work_keys_str_mv |
AT salehi onthemutationloopsofvaluedquivers |
| first_indexed |
2024-04-12T06:26:08Z |
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2024-04-12T06:26:08Z |
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1796109208426381312 |