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Twisted group C*-algebras of acylindrically hyperbolic groups have stable rank one

Sven Raum

Abstract

We prove that the twisted group C*-algebra of an acylindrically hyperbolic group -- not necessarily having trivial finite radical -- has stable rank one.

Twisted group C*-algebras of acylindrically hyperbolic groups have stable rank one

Abstract

We prove that the twisted group C*-algebra of an acylindrically hyperbolic group -- not necessarily having trivial finite radical -- has stable rank one.
Paper Structure (2 sections, 5 theorems, 4 equations)

This paper contains 2 sections, 5 theorems, 4 equations.

Table of Contents

  1. Introduction
  2. Proofs

Key Result

Theorem 1

Let $\Gamma$ be an acylindrically hyperbolic group and $\sigma \in \mathrm{Z}^2(\Gamma)$. Then $\mathrm{C}^*_\mathrm{red}(\Gamma, \sigma)$ has stable rank one.

Theorems & Definitions (8)

  • Theorem 1
  • Proposition 2
  • proof : Proof of Proposition \ref{['prop:transfer-RD-estimate']}
  • Theorem 3: Compare dykemadelaharpe99
  • Corollary 4
  • proof : Proof of Theorem \ref{['thm:acyclindrically-hyperbolic-stable-rank-one']}
  • Corollary 5
  • proof