On embeddings of full amalgamated free product C*–algebras

Armstrong, Scott; Dykema, Ken; Exel, Ruy; Li, Hanfeng

doi:10.1090/S0002-9939-04-07370-8

On embeddings of full amalgamated free product C$^*$–algebras
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by Scott Armstrong, Ken Dykema, Ruy Exel and Hanfeng Li PDF

Proc. Amer. Math. Soc. 132 (2004), 2019-2030 Request permission

Abstract:

We examine the question of when the $*$–homomorphism $\lambda : A*_D B\to \widetilde {A}*_ {\widetilde {D}}\widetilde {B}$ of full amalgamated free product C$^*$–algebras, arising from compatible inclusions of C$^*$–algebras $A\subseteq \widetilde {A}$, $B\subseteq \widetilde {B}$ and $D\subseteq \widetilde {D}$, 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.

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