English

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

Group Theory 2020-05-21 v3 Functional Analysis Operator Algebras

Abstract

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

Keywords

Cite

@article{arxiv.1910.14524,
  title  = {On invertible elements in reduced $C^*$-algebras of acylindrically hyperbolic groups},
  author = {M. Gerasimova and D. Osin},
  journal= {arXiv preprint arXiv:1910.14524},
  year   = {2020}
}