JournalsprimsVol. 49, No. 1pp. 43–85

Periodicities of T-systems and Y-systems, Dilogarithm Identities, and Cluster Algebras II: Types CrC_r, F4F_4, and G2G_2

  • Rei Inoue

    Suzuka University of Medical Science, Japan
  • Osamu Iyama

    Nagoya University, Japan
  • Bernhard Keller

    Université Paris Diderot - Paris 7, France
  • Atsuo Kuniba

    University of Tokyo, Japan
  • Tomoki Nakanishi

    Nagoya University, Nagoya, Chikusa-Ku, Japan
Periodicities of T-systems and Y-systems, Dilogarithm Identities, and Cluster Algebras II: Types $C_r$, $F_4$, and $G_2$ cover
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Abstract

We prove the periodicities of the restricted T-systems and Y-systems associated with the quantum ane algebra of type CrC_r, F4F_4, and G2G_2 at any level. We also prove the dilogarithm identities for these Y-systems at any level. Our proof is based on the tropical Y-systems and the categori cation of the cluster algebra associated with any skew-symmetric matrix by Plamondon.

Cite this article

Rei Inoue, Osamu Iyama, Bernhard Keller, Atsuo Kuniba, Tomoki Nakanishi, Periodicities of T-systems and Y-systems, Dilogarithm Identities, and Cluster Algebras II: Types CrC_r, F4F_4, and G2G_2. Publ. Res. Inst. Math. Sci. 49 (2013), no. 1, pp. 43–85

DOI 10.4171/PRIMS/96