Dynamical Aspects of Lie--Poisson Structures

Details Dynamical Aspects of Lie--Poisson Structures Dynamical Aspects of Lie--Poisson Structures

1993-08-06

arxiv.org/abs/hep-th/9308026v1

Mod.Phys.Lett. A8 (1993) 2973

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, figures not included

Scientific paper

10.1142/S0217732393003391

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 classes of problems. In the first set of examples we consider some hamiltonian systems associated with Lie-Poisson structures and we investigate the equations of the motion. In the second set of examples we consider systems which preserve the chosen bracket, but are dissipative. However in this approach, they survive the quantization procedure.

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