Deformation quantization and quantum groupoids
نویسنده
چکیده
It is shown that a quantum groupoid (or a QUE algebroid, i.e., deformation of the universal enveloping algebra of a Lie algebroid) naturally gives rise to a Lie bialgebroid as a classical limit. The converse question, i.e., the quantization problem, is raised, and it is proved for all regular triangular Lie bialgebroids. For a Poisson manifold P , the existence of a star-product is shown to be equivalent to the existence of a quantization of the corresponding Lie bialgebroid (TP, T ∗P ).
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