Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Purely infinite, simple $C^{*}$-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

Abstract | References | Similar Articles | Additional Information

Abstract: In the reduced free product of C$^{*}$-algebras, $(A,\phi )=(A_{1},\phi _{1})*(A_{2},\phi _{2})$ with respect to faithful states $\phi _{1}$ and $\phi _{2}$, $A$ is purely infinite and simple if $A_{1}$ is a reduced crossed product $B\rtimes _{\alpha ,r}G$ for $G$ an infinite group, if $\phi _{1}$ is well behaved with respect to this crossed product decomposition, if $A_{2}\ne \mathbf{C}$ and if $\phi $ is not a trace.


References [Enhancements On Off] (What's this?)

  • 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 $C^{*}$-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 $C^{*}$-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$^{\ast }$-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

Similar Articles

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

American Mathematical Society