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

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

2010-04-21

arxiv.org/abs/1004.3721v3

Mathematics

Operator Algebras

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

Scientific paper

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.

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