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.
Double Poisson vertex algebras and non-commutative Hamiltonian equations / De Sole, Alberto; V., Kac; Valeri, Daniele. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 281:(2015), pp. 1025-1099. [10.1016/j.aim.2015.05.011]
Double Poisson vertex algebras and non-commutative Hamiltonian equations
DE SOLE, ALBERTO;VALERI, DANIELE
2015
Abstract
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.| File | Dimensione | Formato | |
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