Free products with amalgamation over central C∗-subalgebras

Let A and B be C∗-algebras whose quotients are all RFD (residually finite dimensional), and let C be a central C∗-subalgebra in both A and B. We prove that the full amalgamated free product A∗C B is then RFD. This generalizes Korchagin's result that amalgamated free products of commutative C∗-algebras are RFD. When applied to the case of trivial amalgam, our methods recover the result of Exel and Loring for separable C∗-algebras. As corollaries to our theorem, we give sufficient conditions for amalgamated free products of maximally almost periodic (MAP) groups to have RFD C∗- algebras and hence to be MAP.