A Combinatorial Formula for Certain Elements of Upper Cluster Algebras
We develop an elementary formula for certain non-trivial elements of upper cluster algebras. These elements have positive coefficients. We show that when the cluster algebra is acyclic these elements form a basis. Using this formula, we show that each non-acyclic skew-symmetric cluster algebra of ra...
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| Дата: | 2015 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2015
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147117 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A Combinatorial Formula for Certain Elements of Upper Cluster Algebras / K. Lee, L. Li, M.R. Mills // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 16 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147117 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1471172019-02-14T01:23:40Z A Combinatorial Formula for Certain Elements of Upper Cluster Algebras Lee, K. Li, L. Mills, M.R. We develop an elementary formula for certain non-trivial elements of upper cluster algebras. These elements have positive coefficients. We show that when the cluster algebra is acyclic these elements form a basis. Using this formula, we show that each non-acyclic skew-symmetric cluster algebra of rank 3 is properly contained in its upper cluster algebra. 2015 Article A Combinatorial Formula for Certain Elements of Upper Cluster Algebras / K. Lee, L. Li, M.R. Mills // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 16 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 13F60 DOI:10.3842/SIGMA.2015.049 http://dspace.nbuv.gov.ua/handle/123456789/147117 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We develop an elementary formula for certain non-trivial elements of upper cluster algebras. These elements have positive coefficients. We show that when the cluster algebra is acyclic these elements form a basis. Using this formula, we show that each non-acyclic skew-symmetric cluster algebra of rank 3 is properly contained in its upper cluster algebra. |
| format |
Article |
| author |
Lee, K. Li, L. Mills, M.R. |
| spellingShingle |
Lee, K. Li, L. Mills, M.R. A Combinatorial Formula for Certain Elements of Upper Cluster Algebras Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Lee, K. Li, L. Mills, M.R. |
| author_sort |
Lee, K. |
| title |
A Combinatorial Formula for Certain Elements of Upper Cluster Algebras |
| title_short |
A Combinatorial Formula for Certain Elements of Upper Cluster Algebras |
| title_full |
A Combinatorial Formula for Certain Elements of Upper Cluster Algebras |
| title_fullStr |
A Combinatorial Formula for Certain Elements of Upper Cluster Algebras |
| title_full_unstemmed |
A Combinatorial Formula for Certain Elements of Upper Cluster Algebras |
| title_sort |
combinatorial formula for certain elements of upper cluster algebras |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147117 |
| citation_txt |
A Combinatorial Formula for Certain Elements of Upper Cluster Algebras / K. Lee, L. Li, M.R. Mills // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 16 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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