Strict Quantization of Solvable Symmetric Spaces

2000/10/01 by Pierre Bieliavsky, Bieliavsky, Pierre · 1 citation
Mathematics · Physics and Astronomy · #53C35 (Primary) 81S10 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG) #math-ph #math.DG #math.MP #math.QA #math.SG #msc:53C35 #msc:81S10

paper · pdf · doi:10.48550/arxiv.math/0010004

32 pages, Latex

arxiv created 2000/10/01 · arxiv updated 2009/11/30

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.

Cited by

• Kinematical Lie algebras and symplectic symmetric spaces I: Lie algebraic aspects

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