Difference equations and cluster algebras I: Poisson bracket for integrable difference equations
Quantum Algebra
2011-09-28 v2 Mathematical Physics
math.MP
Abstract
We introduce the cluster algebraic formulation of the integrable difference equations, the discrete Lotka-Volterra equation and the discrete Liouville equation, from the view point of the general T-system and Y-system. We also study the Poisson structure for the cluster algebra, and give the associated Poisson bracket for the two difference equations.
Cite
@article{arxiv.1012.5574,
title = {Difference equations and cluster algebras I: Poisson bracket for integrable difference equations},
author = {Rei Inoue and Tomoki Nakanishi},
journal= {arXiv preprint arXiv:1012.5574},
year = {2011}
}
Comments
21 pages