Strict deformation quantization of locally convex algebras and modules

Lechner, Gandalf ORCID: https://orcid.org/0000-0002-8829-3121 and Waldmann, Stefan 2016. Strict deformation quantization of locally convex algebras and modules. Journal of Geometry and Physics 99 , pp. 111-144. 10.1016/j.geomphys.2015.09.013

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Abstract

In this work various symbol spaces with values in a sequentially complete locally convex vector space are introduced and discussed. They are used to define vector-valued oscillatory integrals which allow to extend Rieffel's strict deformation quantization to the framework of sequentially complete locally convex algebras and modules with separately continuous products and module structures, making use of polynomially bounded actions of ℝn. Several well-known integral formulas for star products are shown to fit into this general setting, and a new class of examples involving compactly supported ℝn-actions on ℝn is constructed.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Locally convex algebra; Deformation quantization; Rieffel construction; Star product
Publisher:	Elsevier
ISSN:	0393-0440
Related URLs:	http://arxiv.org/abs/1109.5950
Date of First Compliant Deposit:	30 March 2016
Date of Acceptance:	26 September 2015
Last Modified:	16 Nov 2024 15:15
URI:	https://orca.cardiff.ac.uk/id/eprint/77633

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