Non-computability of $K$-theory for computably presented C*-algebras

Christopher J. Eagle; Isaac Goldbring; Timothy H. McNicholl; Russell Miller

Non-computability of $K$-theory for computably presented C*-algebras

Operator Algebras 2026-02-18 v2 Logic

Authors: Christopher J. Eagle , Isaac Goldbring , Timothy H. McNicholl , Russell Miller

Abstract

We give an example of a unital C*-algebra $\mathbf{A}$ with a computable presentation and for which neither $K_0(\mathbf{A})$ nor $K_1(\mathbf{A})$ has a computable presentation.

Keywords

graph algebras c*-algebras

Cite

@article{arxiv.2602.06877,
  title  = {Non-computability of $K$-theory for computably presented C*-algebras},
  author = {Christopher J. Eagle and Isaac Goldbring and Timothy H. McNicholl and Russell Miller},
  journal= {arXiv preprint arXiv:2602.06877},
  year   = {2026}
}

Comments

Second draft; the question left open at the end of the previous version has now been solved. 6 pages; comments welcome!

Non-computability of $K$-theory for computably presented C*-algebras

Abstract

Keywords

Cite

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