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Symmetry, Integrability and Geometry: Methods and Applications, 2010, Volume 6, 085, 34 pp.
DOI: https://doi.org/10.3842/SIGMA.2010.085 (Mi sigma543) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Dilogarithm Identities for Sine-Gordon and Reduced Sine-Gordon Y-Systems

Tomoki Nakanishia, Roberto Tateob

a Graduate School of Mathematics, Nagoya University, Nagoya, 464-8604, Japan
b Dipartimento di Fisica Teorica and INFN, Università di Torino, Via P. Giuria 1, 10125 Torino, Italy
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DOI: https://doi.org/10.3842/SIGMA.2010.085
Abstract: We study the family of Y-systems and T-systems associated with the sine-Gordon models and the reduced sine-Gordon models for the parameter of continued fractions with two terms. We formulate these systems by cluster algebras, which turn out to be of finite type, and prove their periodicities and the associated dilogarithm identities which have been conjectured earlier. In particular, this provides new examples of periodicities of seeds.
Keywords: cluster algebras; quantum groups; integrable models.
Received: May 29, 2010; in final form October 16, 2010; Published online October 19, 2010
Bibliographic databases:
Document Type: Article
MSC: 13F60; 17B37
Language: English
Citation: Tomoki Nakanishi, Roberto Tateo, “Dilogarithm Identities for Sine-Gordon and Reduced Sine-Gordon Y-Systems”, SIGMA, 6 (2010), 085, 34 pp.
Citation in format AMSBIB
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\by Tomoki Nakanishi, Roberto Tateo
\paper Dilogarithm Identities for Sine-Gordon and Reduced Sine-Gordon Y-Systems
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    		Symmetry, Integrability and Geometry: Methods and Applications
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