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COMPUTABLE PRESENTATIONS OF C*-ALGEBRAS

Part of: Model theory Selfadjoint operator algebras Computability and recursion theory

Published online by Cambridge University Press:  20 April 2023

ALEC FOX
ALEC FOX*
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA, IRVINE ROWLAND HALL, IRVINE, CA 92697, USA
*
E-mail: foxag@uci.edu
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Abstract

We initiate the study of computable presentations of real and complex C*-algebras under the program of effective metric structure theory. With the group situation as a model, we develop corresponding notions of recursive presentations and word problems for C*-algebras, and show some analogous results hold in this setting. Famously, every finitely generated group with a computable presentation is computably categorical, but we provide a counterexample in the case of C*-algebras. On the other hand, we show every finite-dimensional C*-algebra is computably categorical.

Keywords

C*-algebracomputable structure theoryword problemcomputable categoricity

MSC classification

Primary: 03C57: Effective and recursion-theoretic model theory 03D40: Word problems, etc. 46L05: General theory of $C^*$-algebras
Secondary: 03D78: Computation over the reals

Information

Type
Article
Information
The Journal of Symbolic Logic , Volume 89 , Issue 3 , September 2024 , pp. 1313 - 1338
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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