TL;DR
This paper constructs the first examples of minimal ambient nuclear C*-algebras containing non-nuclear C*-algebras, using generic Cantor systems of infinite free product groups to explore their properties.
Contribution
It introduces the first known minimal ambient nuclear C*-algebras for non-nuclear C*-algebras, expanding understanding of their structure and examples.
Findings
Existence of minimal ambient nuclear C*-algebras for non-nuclear C*-algebras
Construction via generic Cantor systems of infinite free product groups
No proper intermediate C*-algebras in these examples
Abstract
We provide examples of ambient nuclear C*-algebras of non-nuclear C*-algebras with no proper intermediate C*-algebras. In particular this gives the first examples of minimal ambient nuclear C*-algebras of non-nuclear C*-algebras. For this purpose, we study generic Cantor systems of infinite free product groups.
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