Deformation quantization of Heisenberg manifolds
type: Item
instance of: scholarly article
title: Deformation quantization of Heisenberg manifolds
zbMATH Open document ID: 0679.46055
DOI: 10.1007/BF01256492
author: Marc A. Rieffel
published in: Communications in Mathematical Physics
publication date: 1989-01-01T00:00:00Z
review text: The author studies the deformation quantization for a smooth manifold equipped with a Poisson bracket in the \(C^*\)-algebra framework, as examples of non-commutative manifolds. The much studied non-commutative tori is shown to be an example of the strict form of deformation quantization in author's formulation. As main result of the paper, invariant Poisson structures of Heisenberg manifolds under the action of the Heisenberg Lie group are determined and found to fall into two types, leading to different structure of the resulting algebras for deformation quantization. Generalizations to more general situations are studied in detail. Finally, the SO(3) action of the 2-sphere is shown to be rigid, all deformation being commutative.
Mathematics Subject Classification ID: 46L60
Mathematics Subject Classification ID: 81S10
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L80
zbMATH DE Number: 4113316
zbMATH Keywords: deformation quantization
zbMATH Keywords: Poisson bracket
zbMATH Keywords: non-commutative manifolds
zbMATH Keywords: non-commutative tori
zbMATH Keywords: invariant Poisson structures of Heisenberg manifolds under the action of the Heisenberg Lie group
reviewed by: Huzihiro Araki
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01256492
OpenAlex ID: W2086990318
description: scientific article; zbMATH DE number 4113316