On embeddings of full amalgamated free product C ^* algebras Conference Paper

We examine the question of when the * homomorphism : A D B A ~ D ~ B ~ lambda : A*_D B o widetilde {A}*_ {widetilde {D}}widetilde {B} of full amalgamated free product C ^* algebras, arising from compatible inclusions of C ^* algebras A A ~ Asubseteq widetilde {A} , B B ~ Bsubseteq widetilde {B} and D D ~ Dsubseteq widetilde {D} , is an embedding. Results giving sufficient conditions for lambda to be injective, as well as classes of examples where lambda fails to be injective, are obtained. As an application, we give necessary and sufficient conditions for the full amalgamated free product of finite-dimensional C ^* algebras to be residually finite dimensional.