Quantization of the PoissonSU(2) and its Poisson homogeneous space — The 2-sphere |
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Authors: | Albert Jeu-Liang Sheu |
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Affiliation: | (1) Department of Mathematics, University of Kansas, 66045 Lawrence, KS, USA |
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Abstract: | We show that deformation quantizations of the Poisson structures on the Poisson Lie groupSU(2) and its homogeneous space, the 2-sphere, are compatible with Woronowicz's deformation quantization ofSU(2)'s group structure and Podles' deformation quantization of 2-sphere's homogeneous structure, respectively. So in a certain sense the multiplicativity of the Lie Poisson structure onSU(2) at the classical level is preserved under quantization.With an Appendix by Jiang-Hua Lu and Alan Weinstein Department of Mathematics, University of California, Berkely, CA 94720 USAPartially supported by NSF-Grant DMS-8505550 |
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