IUMJ

Title: On reduced amalgamated free products of C*-algebras and the MF property

Authors: Jonas Seebach

Issue: Volume 61 (2012), Issue 5, 1911-1923

Abstract:

We establish the MF property of the reduced group $C^{*}$-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 $C^{*}$-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 $C^{*}$-algebra which is MF.