Deformation Quantization of Certain Non-linear Poisson Structures

Details Deformation Quantization of Certain Non-linear Poisson Structures Deformation Quantization of Certain Non-linear Poisson Structures

1998-02-06

arxiv.org/abs/math/9802034v1

Mathematics

Functional Analysis

AMS-LaTeX v1.2, 26 pages, to appear in International Journal of Mathematics

Scientific paper

As a generalization of the linear Poisson bracket on the dual space of a Lie algebra, we introduce certain non-linear Poisson brackets which are ``cocycle perturbations'' of the linear Poisson bracket. We show that these special Poisson brackets are equivalent to Poisson brackets of central extension type, which resemble the central extensions of an ordinary Lie bracket via Lie algebra cocycles. We are able to formulate (strict) deformation quantizations of these Poisson brackets by means of twisted group C*-algebras. We also indicate that these deformation quantizations can be used to construct some specific non-compact quantum groups.

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