Some Examples of Blackadar and Kirchberg's MF Algebras

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${}^{\ast }$-algebras, whose BDF extension semigroup is not group. These examples include, for example, $C_r^{\ast }(F_n){\otimes }_{max}{C}^{\ast }(F_n)$, $C_r^{\ast }(F_n){\otimes }_{min}{C}^{\ast }(F_n)$, $C_r^{\ast }(H_1\ast H_2)$ 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.

References in corpus (3)

• Topological Free Entropy Dimension in Unital C^* algebras (II) : Orthogonal Sum of Unital C^*-algebras
• Irreducible representations of inner quasidiagonal C*-algebras
• Topological Free Entropy Dimensions in Nuclear C${}^{\ast }$-algebras and in Full Free Products of C${}^{\ast }$-algebras