Crossed Products and MF algebras

TL;DR

This paper proves that crossed products of certain MF algebras by amenable residually finite groups are also MF algebras under almost periodic actions, and provides examples of crossed products with non-group BDF Ext semigroups.

Contribution

It generalizes previous results by establishing the MF property for a broader class of crossed product algebras under specific conditions.

Findings

Crossed products of unital finitely generated MF algebras by amenable residually finite groups are MF.

Constructed examples of crossed product C*-algebras with non-group BDF Ext semigroups.

Abstract

We prove that the crossed product AxG of a unital finitely generated MF algebra A by a discrete finitely generated amenable residually finite group G is an MF algebra, provided that the action is almost periodic. This generalizes a result of Hadwin and Shen. We also construct two examples of crossed product C*-algebras whose BDF Ext semigroups are not groups.