On Reduced Amalgamated Free Products of C*-algebras and the MF-Property

Abstract

We establish the MF property of the reduced group $C^{\ast }$-algebra of an amalgamated free product of countable Abelian discrete groups. This result is then used to give a characterization of the amalgamated free products of Abelian groups for which the BDF semigroup of the reduced group $C^{\ast }$-algebra is a group. Along the way we get a tensor product factorization of the corresponding group von Neumann algebra. We end the exposition by applying the ideas from the first part to give a few more examples of groups with a reduced group $C^{\ast }$-algebra which is MF.

arXiv comment11 pages. Final version. To appear in the Indiana University Mathematics Journal