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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2010
• Main Authors: Nakanishi, T., Tateo, R.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2010
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146519
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Dilogarithm Identities for Sine-Gordon and Reduced Sine-Gordon Y-Systems / T. Nakanishi, R. Tateo // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 36 назв. — англ.

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...