Linearization of Poisson Lie group structures

Compatible Poisson-Lie structures on the loop group of SL2.

Compatible Poisson-Lie structures on the loop group of SL 2. Abstract. We define a 1-parameter family of r-matrices on the loop algebra of sl 2 , defining compatible Poisson structures on the associated loop group, which degenerate into the rational and trigonometric structures, and study the Manin triples associated to them. Introduction. The concept of bi-(or multi-)Hamiltonian structures on ...

Ju n 20 00 Poisson – Lie structures on Galilei group ∗

The complete list of Poisson–Lie structures on 4-d Galilei group is presented.

Poisson Structures on Lie Algebroids

In this paper the properties of Lie algebroids with Poisson structures are investigated. We generalize some results of Fernandes [1] regarding linear contravariant connections on Poisson manifolds at the level of Lie algebroids. In the last part, the notions of complete and horizontal lifts on the prolongation of Lie algebroid are studied and their compatibility conditions are pointed out.

On Linearization of Lie Group Extensions

Dynamical Aspects of Lie – Poisson Structures

Quantum Groups can be constructed by applying the quantization by deformation procedure to Lie groups endowed with a suitable Poisson bracket. Here we try to develop an understanding of these structures by investigating dynamical systems which are associated with this bracket. We look at SU (2) and SU (1, 1), as submanifolds of a 4–dimensional phase space with constraints, and deal with two cla...