Quantum groupoids and deformation quantization

Details Quantum groupoids and deformation quantization Quantum groupoids and deformation quantization

1997-08-19

arxiv.org/abs/q-alg/9708020v2

Mathematics

Quantum Algebra

LaTex, 9 pages, minor changes made and references added (C. R. Acad. Sci. Paris Serie A, to appear)

Scientific paper

10.1016/S0764-4442(97)82982-5

The purpose of this Note is to unify quantum groups and star-products under a general umbrella: quantum groupoids. It is shown that a quantum groupoid naturally gives rise to a Lie bialgebroid as a classical limit. The converse question, i.e., the quantization problem, is posed. In particular, any regular triangular Lie bialgebroid is shown quantizable. For the Lie bialgebroid of a Poisson manifold, its quantization is equivalent to a star-product.

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