Corrigendum to "Classifying C*-algebras with both finite and infinite subquotients"

TL;DR

This corrigendum addresses an error in a previous paper on classifying C*-algebras, providing corrected proofs while confirming that the main results and claims about Morita equivalence and stable isomorphism remain valid.

Contribution

The paper corrects a specific lemma in the original classification work, ensuring the validity of the main results without altering the overall conclusions.

Findings

Corrected the statement of Lemma 4.5

Confirmed main results remain valid after correction

Ensured claims on Morita equivalence are unaffected

Abstract

As recently pointed out by Gabe, a fundamental paper by Elliott and Kucerovsky concerning the absorption theory for C*-algebras contains an error, and as a consequence we must report that Lemma 4.5 in "Classifying C*-algebras with both finite and infinite subquotients" J. Funct. Anal. 265 (2013), no. 3, 449--468 is not true as stated. In this corrigendum, we prove an adjusted statement and explain why the error has no consequences to the main results of that paper. In particular, it is noted that all the authors' claims concerning Morita equivalence or stable isomorphism of graph C*-algebras remain correct as stated.