Research PaperNo Access

Extensions of bundles of C*-algebras

Jeremy Steeger

https://orcid.org/0000-0003-2771-4145

Department of Philosophy, University of Washington, Seattle, WA 98195-3350, USA

E-mail Address: jsteeger@uw.edu

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and

Benjamin Feintzeig

https://orcid.org/0000-0001-7692-5155

Department of Philosophy, University of Washington, Seattle, WA 98195-3350, USA

E-mail Address: bfeintze@uw.edu

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https://doi.org/10.1142/S0129055X21500252Cited by:4 (Source: Crossref)

Abstract

Bundles of C*-algebras can be used to represent limits of physical theories whose algebraic structure depends on the value of a parameter. The primary example is the $ℏ \to 0$ limit of the C*-algebras of physical quantities in quantum theories, represented in the framework of strict deformation quantization. In this paper, we understand such limiting procedures in terms of the extension of a bundle of C*-algebras to some limiting value of a parameter. We prove existence and uniqueness results for such extensions. Moreover, we show that such extensions are functorial for the C*-product, dynamical automorphisms, and the Lie bracket (in the $ℏ \to 0$ case) on the fiber C*-algebras.

Keywords:

AMSC: 17B63, 46L65, 81R10, 81S99

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