Letters in Mathematical Physics

, Volume 71, Issue 1, pp 63–73 | Cite as

Trigonometric Dynamical r-Matrices Over Poisson Lie Base

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Abstract

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

Keywords

Dynamical Yang–Baxter equation Poisson Lie groups Poisson Lie manifolds 
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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of MathematicsBar Ilan UniversityRamat GanIsrael
  2. 2.Max-Planck Institut für MathematikBonnGermany

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