Quantum groupoids and deformation quantization

Abstract

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.

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

References in corpus (2)

• Deformation quantization of Poisson manifolds, I
• Solutions of the quantum dynamical Yang-Baxter equation and dynamical quantum groups

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