TY - JOUR
T1 - Mutations of the cluster algebra of type A1 (1) and the periodic discrete Toda lattice
AU - Nobe, Atsushi
N1 - Funding Information:
This work was partially supported by JSPS KAKENHI Grant Number 26400107.
Publisher Copyright:
© 2016 IOP Publishing Ltd Printed in the UK.
PY - 2016/5/31
Y1 - 2016/5/31
N2 - 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.
AB - 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.
KW - Cluster algebra
KW - QRT map
KW - Toda lattice
KW - elliptic curve
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U2 - 10.1088/1751-8113/49/28/285201
DO - 10.1088/1751-8113/49/28/285201
M3 - Article
AN - SCOPUS:84975060233
SN - 1751-8113
VL - 49
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 28
M1 - 285201
ER -