Reddening Sequences for Banff Quivers and the Class 𝘗
We show that a reddening sequence exists for any quiver that is Banff. Our proof is combinatorial and relies on the triangular extension construction for quivers. The other facts needed are that the existence of a reddening sequence is mutation invariant and passes to induced subquivers. Banff quive...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210701 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Reddening Sequences for Banff Quivers and the Class 𝘗. Eric Bucher and John Machacek. SIGMA 16 (2020), 049, 11 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-210701 |
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Bucher, Eric Machacek, John 2025-12-15T15:24:26Z 2020 Reddening Sequences for Banff Quivers and the Class 𝘗. Eric Bucher and John Machacek. SIGMA 16 (2020), 049, 11 pages 1815-0659 2020 Mathematics Subject Classification: 13F60; 16G20 arXiv:1807.03359 https://nasplib.isofts.kiev.ua/handle/123456789/210701 https://doi.org/10.3842/SIGMA.2020.049 We show that a reddening sequence exists for any quiver that is Banff. Our proof is combinatorial and relies on the triangular extension construction for quivers. The other facts needed are that the existence of a reddening sequence is mutation invariant and passes to induced subquivers. Banff quivers define locally acyclic cluster algebras, which are known to coincide with their upper cluster algebras. The existence of reddening sequences for these quivers is consistent with a conjectural relationship between the existence of a reddening sequence and a cluster algebra's equality with its upper cluster algebra. Our result completes a verification of the conjecture for Banff quivers. We also prove that a certain subclass of quivers within the class 𝘗 defines locally acyclic cluster algebras. The authors wish to thank the anonymous referees for their feedback, which has improved this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Reddening Sequences for Banff Quivers and the Class 𝘗 Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Reddening Sequences for Banff Quivers and the Class 𝘗 |
| spellingShingle |
Reddening Sequences for Banff Quivers and the Class 𝘗 Bucher, Eric Machacek, John |
| title_short |
Reddening Sequences for Banff Quivers and the Class 𝘗 |
| title_full |
Reddening Sequences for Banff Quivers and the Class 𝘗 |
| title_fullStr |
Reddening Sequences for Banff Quivers and the Class 𝘗 |
| title_full_unstemmed |
Reddening Sequences for Banff Quivers and the Class 𝘗 |
| title_sort |
reddening sequences for banff quivers and the class 𝘗 |
| author |
Bucher, Eric Machacek, John |
| author_facet |
Bucher, Eric Machacek, John |
| publishDate |
2020 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We show that a reddening sequence exists for any quiver that is Banff. Our proof is combinatorial and relies on the triangular extension construction for quivers. The other facts needed are that the existence of a reddening sequence is mutation invariant and passes to induced subquivers. Banff quivers define locally acyclic cluster algebras, which are known to coincide with their upper cluster algebras. The existence of reddening sequences for these quivers is consistent with a conjectural relationship between the existence of a reddening sequence and a cluster algebra's equality with its upper cluster algebra. Our result completes a verification of the conjecture for Banff quivers. We also prove that a certain subclass of quivers within the class 𝘗 defines locally acyclic cluster algebras.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210701 |
| citation_txt |
Reddening Sequences for Banff Quivers and the Class 𝘗. Eric Bucher and John Machacek. SIGMA 16 (2020), 049, 11 pages |
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AT buchereric reddeningsequencesforbanffquiversandtheclassp AT machacekjohn reddeningsequencesforbanffquiversandtheclassp |
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2025-12-17T12:04:31Z |
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2025-12-17T12:04:31Z |
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1851756979380289536 |