Jonas Andersen Seebach

arXiv2011

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

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.

math.OA↗

arXiv2009

Extensions of the reduced group C*-algebra of a free product of amenable groups

We prove that the unitary equivalence classes of extensions of C*_r(G) by any sigma-unital stable C"-algebra, taken modulo extensions which split via an asymptotic homomorphism, form a group which can be calculated from the universal coefficient theorem of KK-theory when G is a free product of a countable collection of amenable groups.

math.OA↗