Journal of Symplectic Geometry

Volume 1 (2001)

Number 2

Strict Quantization of Solvable Symmetric Spaces

Pages: 269 – 320

DOI: http://dx.doi.org/10.4310/JSG.2001.v1.n2.a4

Author

Pierre Bieliavsky

Abstract

This work is a contribution to the area of Strict Quantization (in the sense of Rieffel) in the presence of curvature and non-Abelian group actions. More precisely, we use geometry to obtain explicit oscillatory integral formulae for strongly invariant strict deformation quantizations of a class of solvable symplectic symmetric spaces. Each of these quantizations gives rise to a field of (pre)-C*-algebras whose fibers are function algebras which are closed under the deformed product. The symmetry group of the symmetric space acts on each fiber by C*-algebra automorphisms.

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