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

DOI:
https://doi.org/10.1090/S0002-9939-04-07370-8

Published electronically:
January 27, 2004

MathSciNet review:
2053974

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Abstract | References | Similar Articles | Additional Information

Abstract: We examine the question of when the -homomorphism of full amalgamated free product C-algebras, arising from compatible inclusions of C-algebras , and , is an embedding. Results giving sufficient conditions for to be injective, as well as classes of examples where 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.

**1.**B. Blackadar,*Weak expectations and nuclear C**-algebras,*Indiana Univ. Math. J.**27**(1978), 1021-1026. MR**80d:46110****2.**E. Blanchard and K. Dykema,*Embeddings of reduced free products of operator algebras,*Pacific J. Math.**199**(2001), 1-19. MR**2002f:46115****3.**D. Blecher and V. Paulsen,*Explicit construction of universal operator algebras and applications to polynomial factorization,*Proc. Amer. Math. Soc.**112**(1991), 839-850. MR**91j:46093****4.**F. Boca,*Free products of completely positive maps and spectral sets,*J. Funct. Anal.**97**(1991), 251-263. MR**92f:46064****5.**N. P. Brown and K. Dykema,*Popa algebras in free group factors*, J. reine angew. Math., to appear.**6.**M.-D. Choi,*The full C**-algebra of the free group on two generators,*Pacific J. Math.**87**(1980), 41-48. MR**82b:46069****7.**R. Exel and T. Loring,*Finite-dimensional representations of free product C**-algebras*, Internat. J. Math.**3**(1992), 469-476. MR**93f:46091****8.**F. M. Goodman, P. de la Harpe and V.F.R. Jones,*Coxeter graphs and towers of algebras,*Mathematical Sciences Research Institute Publications, vol. 14, Springer-Verlag, New York, 1989. MR**91c:46082****9.**T. Loring,*Lifting solutions to perturbing problems in C**-algebras,*Fields Institute Monographs, vol. 8, American Mathematical Society, Providence, RI, 1997. MR**98a:46090****10.**G. K. Pedersen,*Pullback and pushout constructions in**-algebra theory,*J. Funct. Anal.**167**(1999), 243-344. MR**2000j:46105****11.**D. Voiculescu, Symmetries of some reduced free product -algebras,*Operator Algebras and Their Connections with Topology and Ergodic Theory*, Lecture Notes in Mathematics, Volume 1132, Springer-Verlag, Berlin, 1985, pp. 556-588. MR**87d:46075****12.**D. V. Voiculescu, K. J. Dykema, and A. Nica,*Free Random Variables, A noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups*, CRM Monograph Series**1**, American Mathematical Society, Providence, RI, 1992. MR**94c:46133**

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Additional Information

**Scott Armstrong**

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

Email:
sarm@math.berkeley.edu

**Ken Dykema**

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

Email:
Ken.Dykema@math.tamu.edu

**Ruy Exel**

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

Email:
exel@mtm.ufsc.br

**Hanfeng Li**

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

Email:
hli@fields.toronto.edu

DOI:
https://doi.org/10.1090/S0002-9939-04-07370-8

Received by editor(s):
March 18, 2003

Published electronically:
January 27, 2004

Communicated by:
David R. Larson

Article copyright:
© Copyright 2004
American Mathematical Society