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arxiv: 1410.3325 · v2 · pith:GQAM2OPKnew · submitted 2014-10-13 · 🧮 math-ph · math.MP· math.RA· math.RT· nlin.SI

Double Poisson vertex algebras and non-commutative Hamiltonian equations

Alberto De Sole , Victor G. Kac , Daniele Valeri This is my paper
classification 🧮 math-ph math.MPmath.RAmath.RTnlin.SI
keywords algebrasdoublenon-commutativepoissonvertexhamiltoniantheoryaimed
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We develop the formalism of double Poisson vertex algebras (local and non-local) aimed at the study of non-commutative Hamiltionan PDEs. This is a generalization of the theory of double Poisson algebras, developed by Van den Bergh, which is used in the study of Hamiltonian ODEs. We apply our theory of double Poisson vertex algebras to non-commutative KP and Gelfand-Dickey hierarchies. We also construct the related non-commutative de Rham and variational complexes.

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  1. Coupled double Poisson brackets

    math.QA 2026-05 unverdicted novelty 7.0

    Introduces coupled double Poisson brackets, proves bijection to wheeled Poisson brackets, and gives correspondences to Poisson-left-pre-Lie algebras and Yang-Baxter solutions on free polynomial algebras.