English

Locally universal C*-algebras with computable presentations

Logic 2023-03-07 v1 Computational Complexity Operator Algebras

Abstract

The Kirchberg Embedding Problem (KEP) asks if every C*-algebra embeds into an ultrapower of the Cuntz algebra O2\mathcal{O}_2. In an effort to provide a negative solution to the KEP and motivated by the recent refutation of the Connes Embedding Problem, we establish two computability-theoretic consequences of a positive solution to KEP. Both of our results follow from the a priori weaker assumption that there exists a locally universal C*-algebra with a computable presentation.

Keywords

Cite

@article{arxiv.2303.02301,
  title  = {Locally universal C*-algebras with computable presentations},
  author = {Alec Fox and Isaac Goldbring and Bradd Hart},
  journal= {arXiv preprint arXiv:2303.02301},
  year   = {2023}
}

Comments

12 pages. This paper supercedes an earlier paper by the second and third author (arXiv:2107.14010). First draft; comments welcome!

R2 v1 2026-06-28T09:01:02.179Z