Locally universal C*-algebras with computable presentations

2023/03/04 by Alec Fox, Fox, Alec, Isaac Goldbring +3 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA) #Quantum Mechanics and Applications

paper · pdf · doi:10.48550/arxiv.2303.02301

openalex publication_date 2023/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Kirchberg Embedding Problem (KEP) asks if every C*-algebra embeds into an ultrapower of the Cuntz algebra O₂. 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.

Cited by

• On definability of C*-tensor norms
• The Universal Theory of Locally Universal Tracial von Neumann Algebras is not Computable

Related

• On Kirchberg's Embedding Problem
• The Universal Theory of Locally Universal Tracial von Neumann Algebras is not Computable
• A quantum complexity approach to the Kirchberg Embedding Problem
• A computability-theoretic reformulation of the Connes Embedding Problem
• Computable presentations of C*-algebras