Uniform amenability at infinity holds for free groups and limit groups, implying uniform strong convergence in the operator algebraic sense for convergent sequences of such groups in the marked group space.
Proximality and selflessness for group C*-algebras
5 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We prove that the reduced group C*-algebras of infinite countable discrete groups having topologically-free extreme boundaries, or more generally groups that satisfy certain combinatorial property including all acylindrically hyperbolic groups with no nontrivial finite normal subgroups and all Zariski-dense subgroups of PSL(n,R), are selfless in the sense of L. Robert. This generalizes the recent results of Amrutam, Gao, Kunnawalkam Elayavalli, and Patchell, and of Vigdorovich. We also prove that selflessness is stable under tensor product among exact C*-algebras and that a C*-probability space is selfless provided that it is either simple and purely infinite or simple, exact, Z-stable, and uniquely tracial.
years
2026 5verdicts
UNVERDICTED 5representative 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.
Commensurator groups of torsion-free hyperbolic groups are C*-selfless.
Selflessness of separable tracial C*-algebras equals an approximate finitary condition on traces of unitaries and alternating words, proved via ultrapower diagonalization.
A new Toeplitz exactness theorem provides a general machine to upgrade strong convergence in C*-correspondences.
citing papers explorer
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Uniform amenability at infinity
Uniform amenability at infinity holds for free groups and limit groups, implying uniform strong convergence in the operator algebraic sense for convergent sequences of such groups in the marked group space.
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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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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 equals an approximate finitary condition on traces of unitaries and alternating words, proved via ultrapower diagonalization.
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Toeplitz exactness for strong convergence
A new Toeplitz exactness theorem provides a general machine to upgrade strong convergence in C*-correspondences.