Classifying $C^*$-algebras with both finite and infinite subquotients

Soren Eilers; Gunnar Restorff; Efren Ruiz

doi:10.1016/j.jfa.2013.05.006

Classifying $C^*$-algebras with both finite and infinite subquotients

Operator Algebras 2015-05-28 v3

Authors: Soren Eilers , Gunnar Restorff , Efren Ruiz

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Abstract

We give a classification result for a certain class of $C^{*}$ -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 $C^{*}$ -algebras arising from graphs.

Keywords

c*-algebras classification finite topological spaces subquotients graph algebras separating open sets

Cite

@article{arxiv.1009.4778,
  title  = {Classifying $C^*$-algebras with both finite and infinite subquotients},
  author = {Soren Eilers and Gunnar Restorff and Efren Ruiz},
  journal= {arXiv preprint arXiv:1009.4778},
  year   = {2015}
}

Comments

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

Classifying $C^*$-algebras with both finite and infinite subquotients

Abstract

Keywords

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