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arXiv · 1012.5574

Difference equations and cluster algebras I: Poisson bracket for integrable difference equations

Rei Inoue·Tomoki Nakanishi
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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.

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Rei Inoue, Tomoki Nakanishi. 2011-04-21. Difference equations and cluster algebras I: Poisson bracket for integrable difference equations. https://arxiv.org/abs/1012.5574

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