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On embeddings of full amalgamated free product C$^*$-algebras

Authors: Scott Armstrong, Ken Dykema, Ruy Exel and Hanfeng Li
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 2019-2030
MSC (2000): Primary 46L09
Published electronically: January 27, 2004
MathSciNet review: 2053974
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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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Additional Information

Scott Armstrong
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720

Ken Dykema
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843–3368

Ruy Exel
Affiliation: Departamento de Matematica, Universidade Federal de Santa Catarina, 88040-900 Florianopolis SC, Brazil

Hanfeng Li
Affiliation: Department of Mathematics, University of Toronto, Toronto ON M5S 3G3, Canada

Received by editor(s): March 18, 2003
Published electronically: January 27, 2004
Communicated by: David R. Larson
Article copyright: © Copyright 2004 American Mathematical Society

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