Poisson structures for lifts and periodic reductions of integrable lattice equations

Abstract

We introduce and study suitable Poisson structures for four dimensional maps derived as lifts and specific periodic reductions of integrable lattice equations. These maps are Poisson with respect to these structures and the corresponding integrals are in involution.

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Cited by in corpus (7)

• On non-abelian quadrirational Yang-Baxter maps
• A noncommutative discrete potential KdV lift
• Birational solutions to the set-theoretical 4-simplex equation
• Discrete Lax pairs and hierarchies of integrable difference systems
• Poisson structures for difference equations
• Noncommutative solutions to Zamolodchikov's tetrahedron equation and matrix six-factorisation problems
• A Lax pair of a lattice equation whose entropy vanishes