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 . 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!