Classifying $C^{\ast }$-algebras with both finite and infinite subquotients

Abstract

We give a classification result for a certain class of $C^{\ast }$-algebras $\mathfrak{A}$ over a finite topological space $X$ in which there exists an open set $U$ of $X$ such that $U$ separates the finite and infinite subquotients of $\mathfrak{A}$. We will apply our results to $C^{\ast }$-algebras arising from graphs.

Version III: No changes to the text. We only report that Lemma 4.5 is not correct as stated. See arXiv:1505.05951 for the corrected version of Lemma 4.5. As noted in arXiv:1505.05951, the main results of this paper are true verbatim. Version II: Improved some results in Section 3 and loosened the assumptions in Definition 4.1

References in corpus (5)

• C*-Algebras over Topological Spaces: The Bootstrap Class
• C*-Algebras over Topological Spaces: Filtrated K-Theory
• Classification of Extensions of Classifiable C*-algebras
• Universal coefficient theorems for C*-algebras over finite topological spaces
• Filtrated K-theory for real rank zero C*-algebras

Cited by in corpus (10)

• The complete classification of unital graph $C^{\ast }$-algebras: Geometric and strong
• Geometric classification of graph $C^{\ast }$-algebras over finite graphs
• Strong classification of extensions of classifiable C*-algebras
• The ordered K-theory of a full extension
• Leavitt $R$-algebras over countable graphs embed into $L_{2,R}$
• Strong classification of purely infinite Cuntz-Krieger algebras
• Reduction of filtered K-theory and a characterization of Cuntz-Krieger algebras
• Classification of graph C*-algebras with no more than four primitive ideals
• The Ranges of K-theoretic Invariants for Nonsimple Graph Algebras
• Corrigendum to "Classifying C*-algebras with both finite and infinite subquotients"