-Vectors and Non-Self-Crossing Curves for Acyclic Quivers of Finite Type
Let be an acyclic quiver and k be an algebraically closed field. The indecomposable exceptional modules of the path algebra have been widely studied. The real Schur roots of the root system associated with are the dimension vectors of the indecomposable exceptional modules. It has been shown in [...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2021 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211178 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | -Vectors and Non-Self-Crossing Curves for Acyclic Quivers of Finite Type. Su Ji Hong. SIGMA 17 (2021), 010, 25 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862731351365517312 |
|---|---|
| author | Hong, Su Ji |
| author_facet | Hong, Su Ji |
| citation_txt | -Vectors and Non-Self-Crossing Curves for Acyclic Quivers of Finite Type. Su Ji Hong. SIGMA 17 (2021), 010, 25 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Let be an acyclic quiver and k be an algebraically closed field. The indecomposable exceptional modules of the path algebra have been widely studied. The real Schur roots of the root system associated with are the dimension vectors of the indecomposable exceptional modules. It has been shown in [Nájera Chávez A., Int. Math. Res. Not. 2015 (2015), 1590-1600] that for acyclic quivers, the set of positive -vectors and the set of real Schur roots coincide. To give a diagrammatic description of -vectors, K-H. Lee and K. Lee conjectured that for acyclic quivers, the set of -vectors and the set of roots corresponding to non-self-crossing admissible curves are equivalent as sets [Exp. Math., to appear, arXiv:1703.09113]. In [Adv. Math. 340 (2018), 855-882], A. Felikson and P. Tumarkin proved this conjecture for 2-complete quivers. In this paper, we prove a revised version of the Lee-Lee conjecture for acyclic quivers of type , , and ₆ and ₇.
|
| first_indexed | 2026-04-17T15:17:28Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211178 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T15:17:28Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hong, Su Ji 2025-12-25T13:23:34Z 2021 -Vectors and Non-Self-Crossing Curves for Acyclic Quivers of Finite Type. Su Ji Hong. SIGMA 17 (2021), 010, 25 pages 1815-0659 2020 Mathematics Subject Classification: 13F60; 16G20 arXiv:2006.00627 https://nasplib.isofts.kiev.ua/handle/123456789/211178 https://doi.org/10.3842/SIGMA.2021.010 Let be an acyclic quiver and k be an algebraically closed field. The indecomposable exceptional modules of the path algebra have been widely studied. The real Schur roots of the root system associated with are the dimension vectors of the indecomposable exceptional modules. It has been shown in [Nájera Chávez A., Int. Math. Res. Not. 2015 (2015), 1590-1600] that for acyclic quivers, the set of positive -vectors and the set of real Schur roots coincide. To give a diagrammatic description of -vectors, K-H. Lee and K. Lee conjectured that for acyclic quivers, the set of -vectors and the set of roots corresponding to non-self-crossing admissible curves are equivalent as sets [Exp. Math., to appear, arXiv:1703.09113]. In [Adv. Math. 340 (2018), 855-882], A. Felikson and P. Tumarkin proved this conjecture for 2-complete quivers. In this paper, we prove a revised version of the Lee-Lee conjecture for acyclic quivers of type , , and ₆ and ₇. The author would like to thank Kyungyong Lee for guidance and helpful discussions, Son Nyguen for helpful suggestions, and the referees for numerous helpful comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications -Vectors and Non-Self-Crossing Curves for Acyclic Quivers of Finite Type Article published earlier |
| spellingShingle | -Vectors and Non-Self-Crossing Curves for Acyclic Quivers of Finite Type Hong, Su Ji |
| title | -Vectors and Non-Self-Crossing Curves for Acyclic Quivers of Finite Type |
| title_full | -Vectors and Non-Self-Crossing Curves for Acyclic Quivers of Finite Type |
| title_fullStr | -Vectors and Non-Self-Crossing Curves for Acyclic Quivers of Finite Type |
| title_full_unstemmed | -Vectors and Non-Self-Crossing Curves for Acyclic Quivers of Finite Type |
| title_short | -Vectors and Non-Self-Crossing Curves for Acyclic Quivers of Finite Type |
| title_sort | -vectors and non-self-crossing curves for acyclic quivers of finite type |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211178 |
| work_keys_str_mv | AT hongsuji vectorsandnonselfcrossingcurvesforacyclicquiversoffinitetype |