2022/06/03 by Alec Fox, Fox, Alec · 1 citation
Computer Science · Mathematics · #Computability, Logic, AI Algorithms #Advanced Algebra and Logic #Advanced Topology and Set Theory
paper · pdf · doi:10.48550/arxiv.2206.01415
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.