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arXiv · 2405.17709

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

Jack Spielberg
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Abstract

We solve the isomorphism problem for essential unital $C^*$-algebra extensions of the form $0 \to \mathcal{K} \oplus \mathcal{K} \to E \xrightarrow{\pi} M_n \otimes C(\mathbb{T}) \to 0$. We then relate these to analogs of the Effros Shen AF algebras for rational numbers. This involves $C^*$-algebras constructed from categories of paths built from certain nonsimple continued fraction expansions.

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Jack Spielberg. 2024-05-27. $C^*$-algebra extensions associated to continued fraction expansions of rational numbers. https://arxiv.org/abs/2405.17709

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