670 citations · 3.3k across the 47 of their papers we have counts for
4 papers · 1 filter
Non-local Hamiltonian structures and applications to the theory of integrable systems I
Alberto De Sole, Victor G. Kac
We develop a rigorous theory of non-local Hamiltonian structures, built on the notion of a non-local Poisson vertex algebra. As an application, we find conditions that guarantee ap…
Classical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras
Alberto De Sole, Victor G. Kac, Daniele Valeri
We provide a description of the Drinfeld-Sokolov Hamiltonian reduction for the construction of classical W-algebras within the framework of Poisson vertex algebras. In this context…
Rational matrix pseudodifferential operators
Sylvain Carpentier, Alberto De Sole, Victor G. Kac
The skewfield K(d) of rational pseudodifferential operators over a differential field K is the skewfield of fractions of the algebra of differential operators K[d]. In our previous…
Some algebraic properties of differential operators
Sylvain Carpentier, Alberto De Sole, Victor G. Kac
First, we study the subskewfield of rational pseudodifferential operators over a differential field K generated in the skewfield of pseudodifferential operators over K by the subal…