Trigonometric dynamical r-matrices over Poisson Lie base

Abstract

Let $\g$ be a finite dimensional complex Lie algebra and $ł\subset \g$ a Lie subalgebra equipped with the structure of a factorizable quasitriangular Lie bialgebra. Consider the Lie group $\Exp ł$ with the Semenov-Tjan-Shansky Poisson bracket as a Poisson Lie manifold for the double Lie bialgebra $\Dł$. Let $\Nc_ł(0)\subset ł$ be an open domain parameterizing a neighborhood of the identity in $\Exp ł$ by the exponential map. We present dynamical $r$-matrices with values in $\g\wedge \g$ over the Poisson Lie base manifold $\Nc_ł(0)$.

AMS LaTeX, 8 pages

References in corpus (4)

• Geometry and classification of solutions of the Classical Dynamical Yang-Baxter Equation
• The non-commutative Weil algebra
• The Chiral WZNW Phase Space and its Poisson-Lie Groupoid
• On a Poisson-Lie analogue of the classical dynamical Yang-Baxter equation for self-dual Lie algebras