Compatible Poisson brackets, quadratic Poisson algebras and classical r-matrices - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2008

Compatible Poisson brackets, quadratic Poisson algebras and classical r-matrices

(1) ,
1
T. Skrypnyk
  • Fonction : Auteur

Résumé

We show that for a general quadratic Poisson bracket it is possible to define a lot of associated linear Poisson brackets: linearizations of the initial bracket in the neighborhood of special points. We prove that the constructed linear Poisson brackets are always compatible with the initial quadratic Poisson bracket. We apply the obtained results to the cases of the standard quadratic r-matrix bracket and to classical “twisted reflection algebra” brackets. In the first case we obtain that there exists only one non-equivalent linearization: the standard linear r-matrix bracket and recover well-known result that the standard quadratic and linear r-matrix brackets are compatible.We show that there are a lot of non-equivalent linearizations of the classical twisted Reflection Equation Algebra bracket and all of them are compatible with the initial quadratic bracket.

Fichier principal
Vignette du fichier
chp3a10.10072f978-3-642-00873-3_15.pdf (521.21 Ko) Télécharger le fichier
Origine : Accord explicite pour ce dépôt

Dates et versions

hal-03031608 , version 1 (30-11-2020)

Identifiants

Citer

Vladimir Roubtsov, T. Skrypnyk. Compatible Poisson brackets, quadratic Poisson algebras and classical r-matrices. The Abel symposium 2008, Jun 2008, Tromso, Norway. pp.311 - 333, ⟨10.1007/978-3-642-00873-3_15⟩. ⟨hal-03031608⟩
13 Consultations
126 Téléchargements

Altmetric

Partager

Gmail Facebook Twitter LinkedIn More