منابع مشابه
Quantum groupoids and deformation quantization
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 mani...
متن کاملDeformation quantization and quantum groupoids
It is shown that a quantum groupoid (or a QUE algebroid, i.e., deformation of the universal enveloping algebra of a Lie algebroid) naturally gives rise to a Lie bialgebroid as a classical limit. The converse question, i.e., the quantization problem, is raised, and it is proved for all regular triangular Lie bialgebroids. For a Poisson manifold P , the existence of a star-product is shown to be ...
متن کاملOn Lesieur’s Measured Quantum Groupoids
In his thesis ([L1]), which is published in an expended and revised version ([L2]), Franck Lesieur had introduced a notion of measured quantum groupoid, in the setting of von Neumann algebras, using intensively the notion of pseudo-multiplicative unitary, which had been introduced in a previous article of the author, in collaboration with Jean-Michel Vallin [EV]. In [L2], the axioms given are v...
متن کاملMeasured Quantum Groupoids in Action
Franck Lesieur had introduced in his thesis (now published in an expended and revised version in the Mémoires de la SMF (2007)) a notion of measured quantum groupoid, in the setting of von Neumann algebras and a simplification of Lesieur’s axioms is presented in an appendix of this article. We here develop the notions of actions, crossed-product, and obtain a biduality theorem, following what h...
متن کاملHopf Algebroids and quantum groupoids
We introduce the notion of Hopf algebroids, in which neither the total algebras nor the base algebras are required to be commutative. We give a class of Hopf algebroids associated to module algebras of the Drinfeld doubles of Hopf algebras when the Rmatrices act properly. When this construction is applied to quantum groups, we get examples of quantum groupoids, which are semi-classical limits o...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2001
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s002200000334