Classification of tight $C^{\ast }$-algebras over the one-point compactification of $\mathbb{N}$

Abstract

We prove a strong classification result for a certain class of $C^{\ast }$-algebras with primitive ideal space $\tilde{\mathbb{N}}$, where $\tilde{\mathbb{N}}$ is the one-point compactification of $\mathbb{N}$. This class contains the class of graph $C^{\ast }$-algebras with primitive ideal space $\tilde{\mathbb{N}}$. Along the way, we prove a universal coefficient theorem with ideal-related $K$-theory for $C^{\ast }$-algebras over $\tilde{\mathbb{N}}$ whose $\infty$ fiber has torsion-free $K$-theory.

25 pages