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Quantum Groupoids and Deformation Quantization by Ping Xu is a Mathematics article available to read on EtoBox.
What is Quantum Groupoids and Deformation Quantization about?
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. Groupo'ides quantiques et quantification par d&formation R6sutnC. Cette Note a pour but d'unijier groupes quantiques et stur-prod&s .sous une mPme enseigne : les groupdides quantiques. Nous montrons que tout groupoide quantique admet de munitre noturelle une bigL;hraide de Lie comme limite classique. Le problhne rtfciproque de quantjfication est posk, et nou.s le re'solvons dans le cas des higkbroides de Lie triunguluires r&ulitres. Er$in, quantjfier la big&broiile associe'e ci WIG variltP de Poisson revient ti y constntire un stur-produit. Version frangaise abrbge'e Les tenseurs de Poisson, sous plusieurs aspects, ressemblent aux r-matrices triangulaires classiques de la thkorie des groupes quantiques. La notion de bigkbroi'de de Lie in
Who reads Quantum Groupoids and Deformation Quantization?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Ping Xu
- Publisher
- Elsevier Science; Elsevier ; Elsevier BV (ISSN 0764-4442)
- Published
- 1998
- Language
- EN
- Field
- Mathematics (Physical Sciences)