Topological boundaries of covariant representations

2021/12/17 by Amini, Massoud, Zavar, Sajad
#37C85 #46M10 #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2112.09491

Abstract

We associate a boundary \mathcal B_π,u to each covariant representation (π,u,H) of C^*-dynamical system (G,A,α) and study the action of G on \mathcal B_π,u and its amenability properties. We relate rigidity properties of traces on the associated crossed product C*-algebra to faithfulness of action of the group on this boundary.

Related

• Boundary maps and covariant representations
• Examples of non-amenable, boundary-amenable dynamical systems
• Covariant Representations of C*-algebras and their Compact Automorphism\n Groups
• Extensions and Dilations for C^*-dynamical Systems
• C*-Algebras of Irreversible Dynamical Systems