Double Poisson vertex algebras and non-commutative Hamiltonian equations

Alberto De Sole; Victor G. Kac; Daniele Valeri

doi:10.1016/j.aim.2015.05.011

Double Poisson vertex algebras and non-commutative Hamiltonian equations

Mathematical Physics 2015-12-18 v2 math.MP Rings and Algebras Representation Theory Exactly Solvable and Integrable Systems

Authors: Alberto De Sole , Victor G. Kac , Daniele Valeri

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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.

Keywords

double Poisson vertex algebras non-commutative Hamiltonian PDEs double Poisson algebras KP hierarchy Gelfand-Dickey hierarchy de Rham complex variational complex

Cite

@article{arxiv.1410.3325,
  title  = {Double Poisson vertex algebras and non-commutative Hamiltonian equations},
  author = {Alberto De Sole and Victor G. Kac and Daniele Valeri},
  journal= {arXiv preprint arXiv:1410.3325},
  year   = {2015}
}

Comments

56 pages. Minor editing and corrections and references added following the referee suggestions

Double Poisson vertex algebras and non-commutative Hamiltonian equations

Abstract

Keywords

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