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Type $II_{\infty }$ factors generated by purely infinite simple C*-algebras associated with free groups


Authors: Wojciech Szymanski and Shuang Zhang
Journal: Proc. Amer. Math. Soc. 128 (2000), 813-818
MSC (1991): Primary 46L05
DOI: https://doi.org/10.1090/S0002-9939-99-05074-1
Published electronically: September 27, 1999
MathSciNet review: 1626490
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Abstract: Let $\Gamma = G_{1}*G_{2}*...*G_{n}* ...$ be a free product of at least two but at most countably many cyclic groups. With each such group $\Gamma $ we associate a family of C*-algebras, denoted $C^{*}_{r}(\Gamma,\mathcal{P}_{\Lambda})$ and generated by the reduced group C*-algebra $C^{*}_{r}\Gamma$ and a collection $\mathcal{P}_{\Lambda }$ of projections onto the $\ell ^{2}$-spaces over certain subsets of $\Gamma $. We determine $W^{*}(\Gamma, \mathcal{P}_{\Lambda })$, the weak closure of $C^{*}_{r}(\Gamma, \mathcal{P}_{\Lambda })$ in $\mathcal{L}(\ell ^{2}(\Gamma ))$, and use this result to show that many of the C*-algebras in question are non-nuclear.


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Additional Information

Wojciech Szymanski
Affiliation: Department of Mathematics, The University of Newcastle, Newcastle, New South Wales 2308, Australia

Shuang Zhang
Affiliation: Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0025
Email: zhangs@math.uc.edu

DOI: https://doi.org/10.1090/S0002-9939-99-05074-1
Received by editor(s): April 27, 1998
Published electronically: September 27, 1999
Additional Notes: This research was partially supported by NSF grant DMS - 9225076
Communicated by: David R. Larson
Article copyright: © Copyright 1999 American Mathematical Society

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