Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Growth conditions for freeness of the Furstenberg boundary action

Nazmul Alam, Joseph Gondek, Mehrdad Kalantar, Randy Pham

Abstract

Given a finitely generated group $Γ$ and $g\inΓ$, we prove sufficient conditions in terms of various growth/decay functions for freeness of the action of $g$ on the Furstenberg boundary of $Γ$. In this context, we also give a description of the support of stationary states on the reduced C*-algebra of $Γ$.

Growth conditions for freeness of the Furstenberg boundary action

Abstract

Given a finitely generated group and , we prove sufficient conditions in terms of various growth/decay functions for freeness of the action of on the Furstenberg boundary of . In this context, we also give a description of the support of stationary states on the reduced C*-algebra of .
Paper Structure (4 sections, 12 theorems, 15 equations)

This paper contains 4 sections, 12 theorems, 15 equations.

Table of Contents

  1. Introduction and Main results
  2. A growth criterion for freeness of boundary actions: Proof of Theorem \ref{['thm:freeness']}
  3. Support of stationary states: Proof of Theorem \ref{['thm:Gong']}
  4. Amenable radical and growth of conjugacy classes

Key Result

Theorem A

Let $\Gamma$ be a finitely generated group, let $g\in\Gamma$, and denote by $C=C_\Gamma(g)$ the centralizer of $g$ in $\Gamma$. If for all $\gamma\notin C$, then $g$ acts freely on $\partial_F\Gamma$.

Theorems & Definitions (20)

  • Definition 1
  • Theorem A
  • Corollary A
  • Theorem B
  • Corollary B
  • Lemma 2
  • proof
  • Corollary 3
  • Proposition 4
  • Corollary 5
  • ...and 10 more