English

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.

Keywords

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

R2 v1 2026-06-21T17:04:24.881Z