Some Examples of Blackadar and Kirchberg's MF Algebras

TL;DR

This paper explores examples of MF algebras through tensor products and crossed products, and investigates C*-algebras with non-group BDF extension semigroups, enriching the understanding of their structure.

Contribution

It provides new examples of MF algebras via tensor and crossed products, and identifies C*-algebras with non-group BDF extension semigroups, expanding the class of known examples.

Findings

Examples of MF algebras from tensor and crossed products.

Identification of C*-algebras with non-group BDF extension semigroups.

Extension of known classes of MF algebras and their properties.

Abstract

In the paper, we provide some examples of MF algebras by considering minimal or maximal tensor products of MF algebras and crossed products of MF algebras by finite groups or an integer group. We also present some examples of C$^*$-algebras, whose BDF extension semigroup is not group. These examples include, for example, $ C_r^*(F_n)\otimes_{max} C^*(F_n) $, $ C_r^*(F_n)\otimes_{min} C^*(F_n) $, $C_r^*(H_1\ast H_2)$ with $2\le |H_1|<\infty$ and $3\le |H_2|<\infty$ where $|H_1|$, $|H_2|$ are the orders of thr groups $H1$, or $H_2$ respectively, and many others.