Residually Finite Partial Actions and MF Fell Bundles

TL;DR

This paper explores the MF property and quasidiagonality in cross-sectional C*-algebras derived from Fell Bundles and partial dynamical systems, generalizing residually finite actions to partial systems.

Contribution

It introduces a generalization of residually finite actions to partial topological dynamical systems and analyzes their impact on MF properties in associated C*-algebras.

Findings

Partial Bernoulli shift yields MF reduced crossed product under certain group conditions

Generalization of residually finite actions to partial systems

Conditions for MF property in cross-sectional C*-algebras

Abstract

We study Blackadar and Kirchberg's matricial field (MF) property and quasidiagonality in cross-sectional C*-algebras constructed from Fell Bundles and, in particular, from partial C*-dynamical systems. In doing so we generalize Kerr and Nowak's notion of a residually finite action to partial topological dynamical systems. We look at some examples exhibiting this property including the partial Bernoulli shift which produces an MF reduced crossed product provided the group in question is exact, residually finite, and admits an MF reduced group C*-algebra.