Non-amenable tight squeezes by Kirchberg algebras

Abstract

We give a framework to produce C*-algebra inclusions with extreme properties. This gives the first constructive nuclear minimal ambient C*-algebras. We further obtain a purely infinite analogue of Dadarlat's modeling theorem on AF-algebras: Every Kirchberg algebra is rigidly and KK-equivalently sandwiched by non-nuclear C*-algebras without intermediate C*-algebras. Finally we reveal a novel property of Kirchberg algebras: They embed into arbitrarily wild C*-algebras as rigid maximal C*-subalgebras.

21 pages, minor revision of v2, to appear in Mathematische Annalen

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Cited by in corpus (4)

• Maximal von Neumann subalgebras arising from maximal subgroups
• Crossed product splitting of intermediate operator algebras via 2-cocycles
• Amenable actions on ill-behaved simple C*-algebras
• Simplicity and tracial weights on non-unital reduced crossed products