Vol. 284, No. 2, 2016

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A note on nonunital absorbing extensions

James Gabe

Vol. 284 (2016), No. 2, 383–393

Elliott and Kucerovsky stated that a nonunital extension of separable C -algebras with a stable ideal is nuclearly absorbing if and only if the extension is purely large. However, their proof was flawed. We give a counterexample to their theorem as stated, but establish an equivalent formulation of nuclear absorption under a very mild additional assumption to being purely large. In particular, if the quotient algebra is nonunital, then we show that the original theorem applies. We also examine how this affects results in classification theory.

absorbing extensions, corona factorisation property, KK-theory, classification
Mathematical Subject Classification 2010
Primary: 46L05, 46L35, 46L80
Received: 15 October 2015
Revised: 9 February 2016
Accepted: 11 February 2016
Published: 30 August 2016
James Gabe
Department of Mathematical Sciences
University of Copenhagen
Universitetsparken 5
DK-2100 Copenhagen