ar X iv : q - a lg / 9 70 80 12 v 1 1 2 A ug 1 99 7 Star Products for integrable Poisson Structures on

نویسنده

  • Claus Nowak
چکیده

We prove the existence of a deformation quantization for integrable Poisson structures on R 3 and give a generalization for a special class of three dimensional manifolds. The program of deformation quantization of the function algebra on a sym-plectic manifold extends naturally to manifolds with nonregular Poisson structures. In contrast to symplectic manifolds the existence of star products on nonregular Poisson manifolds, even on R n , is an open problem. Particular examples of quantizable nonregular Poisson structures were found, e.g. a star product for linear Poisson structures [1, 2] which is induced by a star product on the cotangent bundle of a Lie group, and for quadratic Poisson structures in three dimensions [3]. We will give in this letter a proof for the existence of star products for integrable Poisson structures on R 3 and extend this to a class of three dimensional manifolds.

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تاریخ انتشار 1997