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Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 42, No. 2, pp. 407-417 (2001)
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#
Quantum Half-Planes via Deformation Quantization

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Do Ngoc Diep, Nguyen Viet Hai

Institute of Mathematics, National Center for Natural Sciences and Technology, P. O. Box 631, Bo Ho, 10.000, Hanoi, Vietnam, e-mail: dndiep@thevinh.ncst.ac.vn; Haiphong Teacher's Training College, Haiphong City, Vietnam, e-mail: hainviet@yahoo.com

**Abstract:** \font\msbm=msbm10 \def\bbR{\hbox{\msbm R}} We give an idea of constructing irreducible unitary representations of Lie groups by using Fedosov deformation quantization in the concrete case of the group $ Aff(\bbR)$ of affine transformations of the real line. By an exact computation of the star-product and the operator $\hat{\ell}_Z$, we show that the resulting representations exhausted all the irreducible representations of this groups.

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