Corrigendum to: “Classifying \(C^{\ast}\)-algebras with both finite and infinite subquotients”. (English) Zbl 1355.46051
Summary: As recently pointed out by Gabe, a fundamental paper by G. A. Elliott and D. Kucerovsky [Pac. J. Math. 198, No. 2, 385–409 (2001; Zbl 1058.46041)] concerning the absorption theory for \(C^\ast\)-algebras contains an error, and as a consequence we must report that Lemma 4.5 in [ibid. 265, No. 3, 449–468 (2013; Zbl 1294.46052)] 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 the authors [loc. cit.]. In particular, it is noted that all the authors’ claims concerning Morita equivalence or stable isomorphism of graph \(C^\ast\)-algebras remain correct as stated.
MSC:
| 46L35 | Classifications of \(C^*\)-algebras |
| 19K14 | \(K_0\) as an ordered group, traces |
| 19K35 | Kasparov theory (\(KK\)-theory) |
| 46L80 | \(K\)-theory and operator algebras (including cyclic theory) |
References:
| [1] | Eilers, S.; Restorff, G.; Ruiz, E., Classification of extensions of classifiable \(C^\ast \)-algebras, Adv. Math., 222, 2153-2172 (2009) · Zbl 1207.46055 |
| [2] | Eilers, S.; Restorff, G.; Ruiz, E., On graph \(C^\ast \)-algebras with a linear ideal lattice, Bull. Malays. Math. Sci. Soc. (2), 33, 233-241 (2010) · Zbl 1206.46051 |
| [3] | Eilers, S.; Restorff, G.; Ruiz, E., Classifying \(C^\ast \)-algebras with both finite and infinite subquotients, J. Funct. Anal., 265, 3, 449-468 (2013) · Zbl 1294.46052 |
| [4] | Eilers, S.; Restorff, G.; Ruiz, E., The ordered \(K\)-theory of a full extension, Canad. J. Math., 66, 3, 596-625 (2014) · Zbl 1309.46038 |
| [5] | Eilers, S.; Ruiz, E.; Sørensen, A., Amplified graph \(C^\ast \)-algebras, Münster J. Math., 5, 121-150 (2012) · Zbl 1285.46041 |
| [6] | Elliott, G. A.; Kucerovsky, D., An abstract Voiculescu-Brown-Douglas-Fillmore absorption theorem, Pacific J. Math., 198, 385-409 (2001) · Zbl 1058.46041 |
| [7] | Gabe, J., A note on non-unital absorbing extensions, preprint · Zbl 1357.46045 |
| [8] | Restorff, G.; Ruiz, E., On Rørdam’s classification of certain \(C^\ast \)-algebras with one non-trivial ideal II, Math. Scand., 101, 280-292 (2007) · Zbl 1161.46036 |
| [9] | Rørdam, M., Classification of extensions of certain \(C^\ast \)-algebras by their six term exact sequences in \(K\)-theory, Math. Ann., 308, 93-117 (1997) · Zbl 0874.46039 |
| [10] | Zhang, S., \(K_1\)-groups, quasidiagonality, and interpolation by multiplier projections, Trans. Amer. Math. Soc., 325, 2, 793-818 (1991) · Zbl 0673.46050 |
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