TY - JOUR
T1 - Quantum groupoids and deformation quantization
AU - Xu, Ping
N1 - Funding Information:
(*) Research partially supported by NSF grants DMS95-04913 (‘) The author is grateful to Drinfeld for raising this question
PY - 1998/2
Y1 - 1998/2
N2 - 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.
AB - 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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U2 - 10.1016/S0764-4442(97)82982-5
DO - 10.1016/S0764-4442(97)82982-5
M3 - Article
AN - SCOPUS:0031993877
SN - 0764-4442
VL - 326
SP - 289
EP - 294
JO - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
IS - 3
ER -