57 citations · 353 across the 28 of their papers we have counts for
4 papers · 2 filters
Double Poisson vertex algebras and non-commutative Hamiltonian equations
Alberto De Sole, Victor G. Kac, Daniele Valeri
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 d…
Structure of classical (finite and affine) W-algebras
Alberto De Sole, Victor G. Kac, Daniele Valeri
First, we derive an explicit formula for the Poisson bracket of the classical finite W-algebra W^{fin}(g,f), the algebra of polynomial functions on the Slodowy slice associated to…
Adler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras
Alberto De Sole, Victor G. Kac, Daniele Valeri
We put the Adler-Gelfand-Dickey approach to classical W-algebras in the framework of Poisson vertex algebras. We show how to recover the bi-Poisson structure of the KP hierarchy, t…
Integrability of Dirac reduced bi-Hamiltonian equations
Alberto De Sole, Victor G. Kac, Daniele Valeri
First, we give a brief review of the theory of the Lenard-Magri scheme for a non-local bi-Poisson structure and of the theory of Dirac reduction. These theories are used in the rem…