Mutations of the cluster algebra of type A1 (1) and the periodic discrete Toda lattice

Atsushi Nobe*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

A direct connection between two sequences of points, one of which is generated by seed mutations of the cluster algebra of type A1 (1) and the other by time evolutions of the periodic discrete Toda lattice, is explicitly given. In this construction, each of them is realized as an orbit of a QRT map, and specialization of the parameters in the maps and appropriate choices of the initial points relate them. The connection with the periodic discrete Toda lattice enables us a geometric interpretation of the seed mutations of the cluster algebra of type A1 (1) as an addition of points on an elliptic curve.

Original languageEnglish
Article number285201
JournalJournal of Physics A: Mathematical and Theoretical
Volume49
Issue number28
DOIs
Publication statusPublished - 2016 May 31
Externally publishedYes

Keywords

  • Cluster algebra
  • QRT map
  • Toda lattice
  • elliptic curve

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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