$C^*$-algebra extensions associated to continued fraction expansions of rational numbers
Jack Spielberg

TL;DR
This paper solves the isomorphism problem for specific $C^*$-algebra extensions related to continued fraction expansions of rational numbers, connecting them to Effros Shen AF algebras and path categories.
Contribution
It provides a classification of certain $C^*$-algebra extensions associated with continued fractions of rationals, linking them to known AF algebra structures.
Findings
Solved the isomorphism problem for the specified $C^*$-algebra extensions.
Established a connection between these extensions and Effros Shen AF algebras.
Used categories of paths from continued fraction expansions to analyze the algebras.
Abstract
We solve the isomorphism problem for essential unital -algebra extensions of the form . We then relate these to analogs of the Effros Shen AF algebras for rational numbers. This involves -algebras constructed from categories of paths built from certain nonsimple continued fraction expansions.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Logic · Approximation Theory and Sequence Spaces · Advanced Banach Space Theory
