7 papers
Integrable triples in semisimple Lie algebras
Alberto De Sole, Mamuka Jibladze, Victor G. Kac +1
We classify all integrable triples in simple Lie algebras, up to equivalence. The importance of this problem stems from the fact that for each such equivalence class one can constr…
Integrability of classical affine W-algebras
Alberto De Sole, Mamuka Jibladze, Victor G. Kac +1
We prove that all classical affine W-algebras W(g,f), where g is a simple Lie algebra and f is its non-zero nilpotent element, admit an integrable hierarchy of bi-Hamiltonian PDEs,…
-algebras via Lax type operators
Daniele Valeri
-algebras are certain algebraic structures associated to a finite dimensional Lie algebra and a nilpotent element via Hamiltonian reduction. In this note we gi…
p-reduced multicomponent KP hierarchy and classical W-algebras W(gl_N,p)
Sylvain Carpentier, Alberto De Sole, Victor G. Kac +2
For each partition p of an integer N \geq 2, consisting of r parts, an integrable hierarchy of Lax type Hamiltonian PDE has been constructed recently by some of us. In the present…
Local and non-local multiplicative Poisson vertex algebras and differential-difference equations
Alberto De Sole, Victor G. Kac, Daniele Valeri +1
We develop the notions of multiplicative Lie conformal and Poisson vertex algebras, local and non-local, and their connections to the theory of integrable differential-difference H…
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…