57 citations · 353 across the 28 of their papers we have counts for
33 papers
Cohomology of Lie conformal algebroids
Alberto De Sole, Jiefeng Liu, Daniele Valeri
We study Lie conformal algebroids (LCAd) and their representations using the language of lambda-brackets and Lie conformal algebras. We describe several general constructions, such…
Double Poisson (vertex) algebra cohomology
Maxime Fairon, Daniele Valeri
A noncommutative (NC) version of Poisson geometry was initiated by Van den Bergh by introducing at the level of associative algebras the formalism of double Poisson brackets. Their…
Multi-component Hamiltonian difference operators
Matteo Casati, Daniele Valeri
In this paper we study local Hamiltonian operators for multi-component evolutionary differential-difference equations. We address two main problems: the first one is the classifica…
Remarks on intersection numbers and integrable hierarchies. II. Tau-structure
Daniele Valeri, Di Yang
For systems of evolutionary partial differential equations the tau-structure is an important notion which originated from the deep relation between integrable systems and quantum f…
Flat coordinates of algebraic Frobenius manifolds in small dimensions
Misha Feigin, Daniele Valeri, Johan Wright
Orbit spaces of the reflection representation of finite irreducible Coxeter groups provide polynomial Frobenius manifolds. Flat coordinates of the Frobenius metric are Saito po…
Poisson vertex algebras and Hamiltonian PDE
Alberto De Sole, Victor G. Kac, Daniele Valeri
We discuss the theory of Poisson vertex algebras and their generalizations in relation to integrability of Hamiltonian PDE. In particular, we discuss the theory of affine classical…
Adler-Oevel-Ragnisco type operators and Poisson vertex algebras
Alberto De Sole, Victor G. Kac, Daniele Valeri
The theory of triples of Poisson brackets and related integrable systems, based on a classical R-matrix R in End_F(g), where g is a finite dimensional associative algebra over a fi…
Affine Kac-Moody Algebras and Tau-Functions for the Drinfeld-Sokolov Hierarchies: the Matrix-Resolvent Method
Boris Dubrovin, Daniele Valeri, Di Yang
For each affine Kac-Moody algebra of rank , , or , and for every choice of a vertex , , of the corresponding Dynkin diagram, by usi…
Double Multiplicative Poisson Vertex Algebras
Maxime Fairon, Daniele Valeri
We develop the theory of double multiplicative Poisson vertex algebras. These structures, defined at the level of associative algebras, are shown to be such that they induce a clas…
On Lax operators
Alberto De Sole, Victor G. Kac, Daniele Valeri
We define a Lax operator as a monic pseudodifferential operator of order , such that the Lax equations $\dfrac{\partial L(\partial)}{\partial t_k}=[(L^{\frac…
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…
Weakly nonlocal Poisson brackets: tools, examples, computations
Matteo Casati, Paolo Lorenzoni, Daniele Valeri +1
We implement an algorithm for the computation of Schouten bracket of weakly nonlocal Hamiltonian operators in three different computer algebra systems: Maple, Reduce and Mathematic…
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…
Generators of the quantum finite W-algebras in type A
Alberto De Sole, Laura Fedele, Daniele Valeri
We prove a conjecture proposed in [DSKV16] describing the Lax type operator L(z) for the quantum finite W-algebras of gl_N in terms of a PBW generating system for the W-algebra. In…
Invariant measures for the periodic derivative nonlinear Schrödinger equation
Giuseppe Genovese, Renato Lucà, Daniele Valeri
We construct invariant measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation (DNLS) for small data in and we show these mea…
A Lax type operator for quantum finite W-algebras
Alberto De Sole, Victor Kac, Daniele Valeri
For a reductive Lie algebra g, its nilpotent element f and its faithful finite dimensional representation, we construct a Lax operator L(z) with coefficients in the quantum finite…
Classical affine W-algebras and the associated integrable Hamiltonian hierarchies for classical Lie algebras
Alberto De Sole, Victor G. Kac, Daniele Valeri
We prove that any classical affine W-algebra W(g,f), where g is a classical Lie algebra and f is an arbitrary nilpotent element of g, carries an integrable Hamiltonian hierarchy of…
Finite W-algebras for gl_N
Alberto De Sole, Victor G. Kac, Daniele Valeri
We study the quantum finite W-algebras W(gl_N,f), associated to the Lie algebra gl_N, and its arbitrary nilpotent element f. We construct for such an algebra an r_1 x r_1 matrix L(…
MasterPVA and WAlg: Mathematica packages for Poisson vertex algebras and classical affine -algebras
Matteo Casati, Daniele Valeri
We give an introduction to the Mathematica packages "MasterPVA" and "MasterPVAmulti used to compute lambda-brackets in Poisson vertex algebras, which play an important role in the…
Bethe Ansatz and the Spectral Theory of affine Lie algebra--valued connections II. The non simply--laced case
Davide Masoero, Andrea Raimondo, Daniele Valeri
We assess the ODE/IM correspondence for the quantum -KdV model, for a non-simply laced Lie algebra . This is done by studying a meromorphic connection w…