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

zbMath1252.37066arXiv1012.5574MaRDI QIDQ3101838

Rei Inoue, Tomoki Nakanishi

Publication date: 1 December 2011

Full work available at URL: https://arxiv.org/abs/1012.5574

zbMATH Keywords

Poisson structurescluster algebrasintegrable difference equations

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

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Deformations of cluster mutations and invariant presymplectic forms ⋮ Casting light on shadow Somos sequences ⋮ On 2nd-stage quantization of quantum cluster algebras ⋮ Quantum trilogy: discrete Toda, Y-system and chaos ⋮ On reductions of the Hirota-Miwa equation ⋮ Multiple reductions, foliations and the dynamics of cluster maps ⋮ On inner Poisson structures of a quantum cluster algebra without coefficients

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