English

Computable presentations of C*-algebras

Logic 2023-04-17 v2 Operator Algebras

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

Cite

@article{arxiv.2206.01415,
  title  = {Computable presentations of C*-algebras},
  author = {Alec Fox},
  journal= {arXiv preprint arXiv:2206.01415},
  year   = {2023}
}
R2 v1 2026-06-24T11:37:57.819Z