The reduced C*-algebras of free groups F_n for n ≥ 2, and of finitely generated acylindrically hyperbolic groups with trivial finite radical and rapid decay, have strict comparison and are selfless.
Selfless C*-algebras
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abstract
The aim of this note is to advertise a class of simple C*-algebras which includes noteworthy examples such as the Jiang-Su C*-algebra, the infinite dimensional UHF C*-algebras, the reduced group C*-algebra of the free group in infinitely many generators, and the Cuntz algebras.
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Strict comparison in reduced group $C^*$-algebras
The reduced C*-algebras of free groups F_n for n ≥ 2, and of finitely generated acylindrically hyperbolic groups with trivial finite radical and rapid decay, have strict comparison and are selfless.