Comparison of Poisson structures and Poisson-Lie dynamical r-matrices

Abstract

We construct a Poisson isomorphism between the formal Poisson manifolds g^* and G^*, where g is a finite dimensional quasitriangular Lie bialgebra. Here g^* is equipped with its Lie-Poisson (or Kostant-Kirillov-Souriau) structure, and G^* with its Poisson-Lie structure. We also quantize Poisson-Lie dynamical r-matrices of Balog-Feher-Palla.

9 pages

References in corpus (2)

• The non-commutative Weil algebra
• Stokes Matrices and Poisson Lie Groups

Cited by in corpus (2)

• Ginzburg-Weinstein via Gelfand-Zeitlin
• Irregular Riemann-Hilbert correspondence, Alekseev-Meinrenken dynamical r-matrices and Drinfeld twists