Chapitre D'ouvrage Année : 2013

Double Poisson brackets on free associative algebras

Alexander Odesskii
  • Fonction : Auteur
Vladimir Sokolov

Résumé

We discuss double Poisson structures in sense of M. Van den Berghon free associative algebras focusing on the case of quadratic Poisson brackets.We establish their relations with an associative version of Yang-Baxter equa-tions, we study a bi-hamiltonian property of the linear-quadratic pencil of thedouble Poisson structure and propose a classification of the quadratic doublePoisson brackets in the case of the algebra with two free generators. Manynew examples of quadratic double Poisson brackets are proposed.

Fichier principal
Vignette du fichier
odesskiisokolovcontempams.pdf (249.8 Ko) Télécharger le fichier
Origine Accord explicite pour ce dépôt
Licence

Dates et versions

hal-03038382 , version 1 (03-12-2020)

Licence

Identifiants

Citer

Alexander Odesskii, Vladimir Roubtsov, Vladimir Sokolov. Double Poisson brackets on free associative algebras. Arkady Berenstein, Vladimir Retakh. Noncommutative Birational Geometry, Representations and Combinatorics, 592, American Mathematical Society, pp.225-239, 2013, Contemporary Mathematics ; 592, 978-0-8218-8980-0. ⟨10.1090/conm/592⟩. ⟨hal-03038382⟩
84 Consultations
538 Téléchargements

Altmetric

Partager

  • More