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COMPUTABLE PRESENTATIONS OF C*-ALGEBRAS
Published online by Cambridge University Press: 20 April 2023
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.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic