46 citations · 97 across the 5 of their papers we have counts for
5 papers
On the structure of quantum vertex algebras
Alberto De Sole, Matteo Gardini, Victor G. Kac
A definition of a quantum vertex algebra, which is a deformation of a vertex algebra, was proposed by Etingof and Kazhdan in 1998. In a nutshell, a quantum vertex algebra is a brai…
Poisson -brackets for differential-difference equations
Alberto De Sole, Victor G. Kac, Daniele Valeri +1
We introduce the notion of a multiplicative Poisson -bracket, which plays the same role in the theory of Hamiltonian differential-difference equations as the usual Poisson -b…
Dirac reduction for Poisson vertex algebras
Alberto De Sole, Victor G. Kac, Daniele Valeri
We construct an analogue of Dirac's reduction for an arbitrary local or non-local Poisson bracket in the general setup of non-local Poisson vertex algebras. This leads to Dirac's r…
Classical W-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents
Alberto De Sole, Victor G. Kac, Daniele Valeri
We derive explicit formulas for lambda-brackets of the affine classical W-algebras attached to the minimal and short nilpotent elements of any simple Lie algebra g. This is used to…
Freely generated vertex algebras and non-linear Lie conformal algebras
Alberto De Sole, Victor Kac
We introduce the notion of a non--linear Lie conformal superalgebra and prove a PBW theorem for its universal enveloping vertex algebra. We also show that conversely any graded fre…