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A Combinatorial Formula for Certain Elements of Upper Cluster Algebras
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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A Combinatorial Formula for Certain Elements of Upper Cluster Algebras
Інший ID:
2010 Mathematics Subject Classification: 13F60
DOI:10.3842/SIGMA.2015.049
DOI:10.3842/SIGMA.2015.049
Посилання:
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.
Підтримка:
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.
Дата:
2015
Переглядів:
638
Завантажень:
238
Анотація:
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.
