Every selfless C*-algebra is either stable rank one (tracial case) or purely infinite simple (nontracial case); non-faithful selfless states are shown to land in the purely infinite class.
de la Harpe, Groupes hyperboliques, alg` ebres d’op´ erateurs et un th´ eor` eme de Jolissaint
9 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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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.
Reduced twisted group C*-algebras of groups with property P_PHP are completely selfless, and those of finite-by-G extensions have stable rank one and are pure.
q-Gaussian C*-algebras for |q|<1 are shown to satisfy the Dixmier averaging property and therefore are simple with a unique trace, via rapid decay and spectral gap estimates from free probability.
Commensurator groups of torsion-free hyperbolic groups are C*-selfless.
Certain crossed products of C(X,D) by minimal homeomorphisms and compact group actions with Rokhlin-type properties are pure C*-algebras with stable rank one.
Separable type III_1 factors with trivial bicentralizer are selfless W*-probability spaces for every faithful normal state.
Selflessness of separable tracial C*-algebras is equivalent to approximate selflessness via a finitary condition proved by diagonalization in the tracial ultrapower.
Reduced twisted group C*-algebras of selfless groups with rapid decay are selfless, implying that those of acylindrically hyperbolic groups with rapid decay are pure and have strict comparison.
citing papers explorer
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The Selfless Dichotomy
Every selfless C*-algebra is either stable rank one (tracial case) or purely infinite simple (nontracial case); non-faithful selfless states are shown to land in the purely infinite class.
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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.
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Pureness and stable rank one for reduced twisted group $\mathrm{C}^\ast$-algebras of certain group extensions
Reduced twisted group C*-algebras of groups with property P_PHP are completely selfless, and those of finite-by-G extensions have stable rank one and are pure.
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Simplicity of q-Gaussian C*-algebras
q-Gaussian C*-algebras for |q|<1 are shown to satisfy the Dixmier averaging property and therefore are simple with a unique trace, via rapid decay and spectral gap estimates from free probability.
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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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Pureness of Certain Crossed Product C*-Algebras
Certain crossed products of C(X,D) by minimal homeomorphisms and compact group actions with Rokhlin-type properties are pure C*-algebras with stable rank one.
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Selfless W$^*$-probability spaces and Connes' bicentralizer problem
Separable type III_1 factors with trivial bicentralizer are selfless W*-probability spaces for every faithful normal state.
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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.
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Strict comparison for twisted group C*-algebras
Reduced twisted group C*-algebras of selfless groups with rapid decay are selfless, implying that those of acylindrically hyperbolic groups with rapid decay are pure and have strict comparison.