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 reducedC ∗-algebras of linear groups.arXiv:2602.10616
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
It is shown that the reduced C*-algebra of a nontrivial linear group $\Gamma<GL_{d}(k)$ with trivial amenable radical is selfless. Thus selflessness and simplicity coincide for reduced C*-algebras of linear groups. Similar results are obtained for twisted reduced group C*-algebra.
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UNVERDICTED 2representative citing papers
A general family of selfless inclusions is established for reduced amalgamated free products of C*-algebras, with applications to new HNN extensions and selflessness for graph products over suitable graphs.
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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 reduced amalgamated free products and HNN extensions
A general family of selfless inclusions is established for reduced amalgamated free products of C*-algebras, with applications to new HNN extensions and selflessness for graph products over suitable graphs.