A note on nonunital absorbing extensions

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Abstract

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.

Original languageEnglish
JournalPacific Journal of Mathematics
Volume284
Issue number2
Pages (from-to)383-393
ISSN0030-8730
DOIs
Publication statusPublished - 30. Aug 2016

Keywords

  • Absorbing extensions
  • Classification
  • Corona factorisation property
  • KK-theory

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