## 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 language | English |
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Article number | 285201 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 49 |

Issue number | 28 |

DOIs | |

Publication status | Published - 2016 May 31 |

Externally published | Yes |

## 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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