Type 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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a free product of at least two but at most countably many cyclic groups. With each such group we associate a family of C*-algebras, denoted and generated by the reduced group C*-algebra and a collection of projections onto the -spaces over certain subsets of . We determine , the weak closure of in , and use this result to show that many of the C*-algebras in question are non-nuclear.

**1.**J. Bunce,*Finite operators and amenable C*-algebras*, Proc. Amer. Math. Soc.**56**(1976), 145-151. MR**53:6333****2.**M. D. Choi,*A simple C*-algebra generated by two finite-order unitaries*, Canad. J. Math.**31**(1979), 867-880. MR**80j:46092****3.**M. D. Choi and E. G. Effros,*Nuclear C*-algebras and injectivity: the general case*, Indiana Univ. Math. J.**26**(1977), 443-446. MR**55:3799****4.**A. Connes,*Classification of injective factors*, Ann. of Math.**104**(1976), 73-115. MR**56:12908****5.**J. Cuntz,*K-theory for certain -algebras*, Ann. of Math.**113**(1981), 181-197. MR**84c:46058****6.**G. A. Elliott,*A classification of certain simple C*-algebras*, J. reine angew. Math.**443**(1993), 179-219. MR**94i:46074****7.**G. A. Elliott and M. Rørdam,*Classification of certain infinite simple C*-algebras, II*, Comment. Math. Helv.**70**(1995), 615-638. MR**96e:46080b****8.**R. V. Kadison and J. R. Ringrose,*Fundamentals of the theory of operator algebras, Vol. I, II*, Pure and Applied Mathematics, A Series of Monographs and Textbooks, Academic Press, Inc. (1986). MR**98f:46001a**; MR**96f:46001b****9.**E. Kirchberg,*The classification of purely infinite C*-algebras using Kasparov's theory (preprint)*.**10.**C. Lance,*Tensor products and nuclear C*-algebras*, Operator Algebras and Applications (ed. R. V. Kadison), Proc. Symp. Pure Math., Part I**38**(1981), 379-399.**11.**C. Lance,*On nuclear C*-algebras*, J. Funct. Anal.**12**(1973), 157-176. MR**49:9640****12.**W. L. Paschke and N. Salinas,*C*-algebras associated with free products of groups*, Pac. J. Math.**82**(1979), 211-221. MR**82c:22010****13.**N. C. Phillips,*Classification of purely infinnite simple C*-algebras*, preprint, 1994.**14.**M. Rørdam,*Classification of inductive limits of Cuntz algebras*, J. reine angew. Math.**440**(1993), 175-200. MR**94k:46120****15.**J. Spielberg,*Free-product groups, Cuntz-Krieger algebras, and covariant maps*, Internat. J. Math.**2**(1991), 457-476. MR**92j:46120****16.**W. Szyma\'{n}ski and S. Zhang,*Infinite simple C*-algebras and reduced cross products of abelian C*-algebras and free groups*, Manuscripta Math.**92**(1997), 487-514. MR**98a:46073****17.**S. Zhang,*Purely infinite simple C*-algebras arising from reduced group C*-algebras*, Contemp. Math.**228**(1998), 365-389. CMP**99:07****18.**S. Zhang,*C*-algebras generated by a projection and the reduced group C*-algebras and*, preprint, 1994.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
46L05

Retrieve articles in all journals with MSC (1991): 46L05

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