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Moscow Mathematical Journal, 2004, Volume 4, Number 4, Pages 947–974
DOI: https://doi.org/10.17323/1609-4514-2004-4-4-947-974 (Mi mmj178) 		 
This article is cited in 86 scientific papers (total in 86 papers)

Positivity and canonical bases in rank 2 cluster algebras of finite and affine types

P. Sherman, A. V. Zelevinskii

Northeastern University
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DOI: https://doi.org/10.17323/1609-4514-2004-4-4-947-974
Abstract: The main motivation for the study of cluster algebras initiated in [6], [3], [1] was to design an algebraic framework for understanding total positivity and canonical bases in semisimple algebraic groups. In this paper, we introduce and explicitly construct the canonical basis for a special family of cluster algebras of rank 2.
Key words and phrases: Cluster algebras, affine root systems, Newton polygons.
Received: July 9, 2003; in revised form December 14, 2003
Bibliographic databases:
MSC: Primary 16S99; Secondary 05E15, 22E46
Language: English
Citation: P. Sherman, A. V. Zelevinskii, “Positivity and canonical bases in rank 2 cluster algebras of finite and affine types”, Mosc. Math. J., 4:4 (2004), 947–974
Citation in format AMSBIB
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\by P.~Sherman, A.~V.~Zelevinskii
\paper Positivity and canonical bases in rank~2 cluster algebras of finite and affine types
\jour Mosc. Math.~J.
\yr 2004
\vol 4
\issue 4
\pages 947--974
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\crossref{https://doi.org/10.17323/1609-4514-2004-4-4-947-974}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2124174}
\zmath{https://zbmath.org/?q=an:1103.16018}
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