Groupoïdes quantiques et quantification par déformation

Translated title of the contribution: Quantum groupoids and deformation quantization

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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.

Translated title of the contributionQuantum groupoids and deformation quantization
Original languageFrench
Pages (from-to)289-294
Number of pages6
JournalComptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume326
Issue number3
DOIs
StatePublished - Feb 1998

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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