منابع مشابه
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.
متن کاملPoisson-Lie Structures and Quantisation with Constraints
We develop here a simple quantisation formalism that make use of Lie algebra properties of the Poisson bracket. When the brackets {H,φi} and {φi, φj}, where H is the Hamiltonian and φi are primary and secondary constraints, can be expressed as functions of H and φi themselves, the Poisson bracket defines a Poisson-Lie structure. When this algebra has a finite dimension a system of first order p...
متن کاملDynamical 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...
متن کاملSymplectic Structures Associated to Lie-poisson Groups
The Lie-Poisson analogues of the cotangent bundle and coadjoint orbits of a Lie group are considered. For the natural Poisson brackets the symplectic leaves in these manifolds are classified and the corresponding symplectic forms are described. Thus the construction of the Kirillov symplectic form is generalized for Lie-Poisson groups. On leave of absence from LOMI, Fontanka 27, St.Petersburg, ...
متن کاملComparison of Poisson Structures and Poisson - Lie Dynamical
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 the Poisson-Lie dynamical r-matrices of Balog-Fehér-Palla.
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ژورنال
عنوان ژورنال: Annales Scientifiques de l’École Normale Supérieure
سال: 1997
ISSN: 0012-9593
DOI: 10.1016/s0012-9593(97)89921-1