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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2015 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147117 |
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| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862648489736929280 |
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| author | Lee, K. Li, L. Mills, M.R. |
| author_facet | Lee, K. Li, L. Mills, M.R. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-01T14:51:58Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147117 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T14:51:58Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Lee, K. Li, L. Mills, M.R. 2019-02-13T16:57:08Z 2019-02-13T16:57:08Z 2015 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 https://nasplib.isofts.kiev.ua/handle/123456789/147117 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. This paper is a contribution to the Special Issue on New Directions in Lie Theory. The full collection is
 available at http://www.emis.de/journals/SIGMA/LieTheory2014.html.
 The authors are grateful to the anonymous referees for carefully reading through the manuscript
 and giving us many constructive suggestions to improve the presentation. KL is supported by
 Wayne State University, Korea Institute for Advanced Study, AMS Centennial Fellowship and
 NSA grant H98230-14-1-0323. MM is supported by GAANN Fellowship. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Combinatorial Formula for Certain Elements of Upper Cluster Algebras Article published earlier |
| spellingShingle | A Combinatorial Formula for Certain Elements of Upper Cluster Algebras Lee, K. Li, L. Mills, M.R. |
| title | 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_short | A Combinatorial Formula for Certain Elements of Upper Cluster Algebras |
| title_sort | combinatorial formula for certain elements of upper cluster algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147117 |
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