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

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

2010-12-27

arxiv.org/abs/1012.5574v2

RIMS Kokyuroku Bessatsu B28 (2011) 63-88

Mathematics

Quantum Algebra

21 pages

Scientific paper

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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