# Double Poisson vertex algebras and non-commutative Hamiltonian equations

@article{Sole2015DoublePV, title={Double Poisson vertex algebras and non-commutative Hamiltonian equations}, author={Alberto De Sole and Victor G. Kac and Daniele Valeri}, journal={Advances in Mathematics}, year={2015}, volume={281}, pages={1025-1099} }

## 22 Citations

Double Multiplicative Poisson Vertex Algebras

- Mathematics
- 2021

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 classical structure of…

Hamiltonian Structures for Integrable Nonabelian Difference Equations

- MathematicsCommunications in Mathematical Physics
- 2022

In this paper we extensively study the notion of Hamiltonian structure for nonabelian differential-difference systems, exploring the link between the different algebraic (in terms of double Poisson…

Double Lie algebras of a nonzero weight

- Mathematics
- 2021

We introduce the notion of λ-double Lie algebra, which coincides with usual double Lie algebra when λ = 0. We state that every λ-double Lie algebra for λ 6= 0 provides the structure of modified…

Noncommutative Poisson vertex algebras and Courant-Dorfman algebras

- Mathematics
- 2021

We introduce double Courant–Dorfman algebras, which are noncommutative versions of Roytenberg’s Courant–Dorfman algebras, since we prove that they satisfy the Kontsevich–Rosenberg principle. In…

A New Scheme of Integrability for (bi)Hamiltonian PDE

- Mathematics
- 2015

We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian…

Classical and Quantum $${\mathcal {W}}$$-Algebras and Applications to Hamiltonian Equations

- MathematicsSpringer INdAM Series
- 2019

We start by giving an overview of the four fundamental physical theories, namely classical mechanics, quantum mechanics, classical field theory and quantum field theory, and the corresponding…

Supersymmetric Bi-Hamiltonian Systems

- Mathematics
- 2019

We construct super Hamiltonian integrable systems within the theory of Supersymmetric Poisson vertex algebras (SUSY PVAs). We provide a powerful tool for the understanding of SUSY PVAs called the…

Non-commutative Courant algebroids and Quiver algebras

- Mathematics
- 2017

In this paper, we develop a differential-graded symplectic (Batalin-Vilkovisky) version of the framework of Crawley-Boevey, Etingof and Ginzburg on noncommutative differential geometry based on…

Symmetry approach to integrability and non-associative algebraic structures

- Mathematics
- 2017

The first part of the book is devoted to the symmetry approach to classification of scalar integrable evolution PDEs with two independent variables. In the second part systems of evolution equations…

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