Classical and Quantum Dilogarithm Identities

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2011
• Main Authors: Kashaev, R.M., Nakanishi, T.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2011
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147994
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Classical and Quantum Dilogarithm Identities / R.M. Kashaev, T. Nakanishi // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 65 назв. — англ.

Using the quantum cluster algebra formalism of Fock and Goncharov, we present several forms of quantum dilogarithm identities associated with periodicities in quantum cluster algebras, namely, the tropical, universal, and local forms. We then demonstrate how classical dilogarithm identities naturall...