Purely infinite, simple -algebras arising from free product constructions. III

Authors:
Marie Choda and Kenneth J. Dykema

Journal:
Proc. Amer. Math. Soc. **128** (2000), 3269-3273

MSC (2000):
Primary 46L09; Secondary 46L54

DOI:
https://doi.org/10.1090/S0002-9939-00-05556-8

Published electronically:
May 2, 2000

MathSciNet review:
1707512

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In the reduced free product of C-algebras, with respect to faithful states and , is purely infinite and simple if is a reduced crossed product for an infinite group, if is well behaved with respect to this crossed product decomposition, if and if is not a trace.

**1.**D. Avitzour,*Free products of C**-algebras*, Trans. Amer. Math. Soc.**271**(1982), 423-465. MR**83h:46070****2.**H. Bercovici, D. Voiculescu,*Superconvergence to the free central limit theorem and failure of Cramér theorem for free random variables*, Prob. Theory Relat. Fields**102**(1995), 215-222. MR**96k:46115****3.**J. Cuntz,*K-theory for certain C**-algebras*, Ann. of Math.**113**(1981), 181-197. MR**84c:46058****4.**K.J. Dykema,*Faithfulness of free product states*, J. Funct. Anal.**154**(1998), 223-229. MR**99e:46066****5.**-,*Purely infinite simple**-algebras arising from free product constructions, II*, Math. Scand. (to appear).**6.**K.J. Dykema, U. Haagerup, M. Rørdam,*The stable rank of some free product C**-algebras*, Duke Math. J.**90**(1997), 95-121;*correction*, vol. 94, 1998, p. 213. MR**99g:46077a****7.**K.J. Dykema, M. Rørdam,*Purely infinite simple**-algebras arising from free product constructions*, Can. J. Math.**50**(1998), 323-341. MR**99d:46074****8.**-,*Projections in free product C**-algebras*, Geom. Funct. Anal.**8**(1998), 1-16. MR**99d:46075****9.**-,*Projections in free product C**-algebras, II*, Math. Z. (to appear).**10.**A. Kishimoto, A. Kumjian,*Crossed products of Cuntz algebras by quasi-free automorphisms*, Fields Inst. Commun.**13**(1997), 173-192. MR**98h:46076****11.**D. Voiculescu,*Symmetries of some reduced free product C**-algebras*, Operator Algebras and Their Connections with Topology and Ergodic Theory, Lecture Notes in Mathematics, vol. 1132, Springer-Verlag, 1985, pp. 556-588. MR**87d:46075****12.**D. Voiculescu, K.J. Dykema, A. Nica,*Free Random Variables*, CRM Monograph Series vol. 1, American Mathematical Society, 1992. MR**94c:46133**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
46L09,
46L54

Retrieve articles in all journals with MSC (2000): 46L09, 46L54

Additional Information

**Marie Choda**

Affiliation:
Department of Mathematics, Osaka Kyoiku University, Asahigaoka, Kashiwara 582, Japan

Email:
marie@cc.osaka-kyoiku.ac.jp

**Kenneth J. Dykema**

Affiliation:
Department of Mathematics and Computer Science, Odense University, DK-5230 Odense M, Denmark

Address at time of publication:
Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368

Email:
ken.dykema@math.tamu.edu

DOI:
https://doi.org/10.1090/S0002-9939-00-05556-8

Received by editor(s):
December 17, 1998

Published electronically:
May 2, 2000

Communicated by:
David R. Larson

Article copyright:
© Copyright 2000
American Mathematical Society