# Non-amenable tight squeezes by Kirchberg algebras

## TL;DR

This paper introduces a framework for constructing C*-algebra inclusions with extreme properties, including the first nuclear minimal ambient C*-algebras and novel embeddings of Kirchberg algebras into wild C*-algebras.

## Contribution

It provides the first constructive nuclear minimal ambient C*-algebras and a purely infinite analogue of Dadarlat's AF-algebra modeling theorem, revealing new properties of Kirchberg algebras.

## Key findings

- Constructed nuclear minimal ambient C*-algebras.
- Established a purely infinite analogue of Dadarlat's theorem.
- Showed Kirchberg algebras embed into arbitrarily wild C*-algebras as rigid maximal subalgebras.

## 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.