Nonfaithful selfless C*-probability spaces are purely infinite and simple, so every selfless C*-algebra is either purely infinite or stably finite and hence pure.
Selfless reduced amalgamated free products and HNN extensions
3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We find a general family of selfless inclusions in reduced amalgamated free products of C*-algebras. Apart from generalizing prior works due to McClanahan, Ivanov and Omland, our work yields a few other applications. We present a short new approach to construct HNN extensions of C*-algebras and find several new examples of selflessness using this. This generalizes results of Ueda, Ivanov and de la Harpe-Preaux. As another application our work yields a short proof of selflessness for arbitrary graph products of C*-algebras over graphs of more than 2 vertices and diameter greater than 3.
years
2026 3verdicts
UNVERDICTED 3representative citing papers
Commensurator groups of torsion-free hyperbolic groups are C*-selfless.
Selflessness of separable tracial C*-algebras is equivalent to approximate selflessness via a finitary condition proved by diagonalization in the tracial ultrapower.
citing papers explorer
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The Selfless Dichotomy
Nonfaithful selfless C*-probability spaces are purely infinite and simple, so every selfless C*-algebra is either purely infinite or stably finite and hence pure.
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Selfless inclusions arising from commensurator groups of hyperbolic groups
Commensurator groups of torsion-free hyperbolic groups are C*-selfless.
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A finitary criterion for selfless tracial C*-algebras
Selflessness of separable tracial C*-algebras is equivalent to approximate selflessness via a finitary condition proved by diagonalization in the tracial ultrapower.