On invertible elements in reduced C^*-algebras of acylindrically hyperbolic groups

2019/10/31 by Gerasimova, M., Osin, D. · 3 citations
#FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1910.14524

Abstract

Let G be an acylindrically hyperbolic group. We prove that if G has no non-trivial finite normal subgroups, then the set of invertible elements is dense in the reduced C^∗-algebra of G. The same result is obtained for finite direct products of acylindrically hyperbolic groups.

Cited by

• An extreme boundary of acylindrically hyperbolic groups
• Extensions of pure C*-algebras
• Strict comparison for twisted group C*-algebras

Related

• Invariant subalgebras of the reduced group C^*-algebra
• New holomorphically closed subalgebras of C^*-algebras of hyperbolic groups
• Normal subgroups of invertibles and of unitaries in a C*-algebra
• Relatively compact sets in the reduced C^∗-algebras of Coxeter groups
• Twisted group C*-algebras of acylindrically hyperbolic groups have stable rank one