Purely infinite, simple $C^{*}$-algebras arising from free product constructions. III
HTML articles powered by AMS MathViewer
- by Marie Choda and Kenneth J. Dykema PDF
- Proc. Amer. Math. Soc. 128 (2000), 3269-3273 Request permission
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
- Daniel Avitzour, Free products of $C^{\ast }$-algebras, Trans. Amer. Math. Soc. 271 (1982), no. 2, 423–435. MR 654842, DOI 10.1090/S0002-9947-1982-0654842-1
- H. Bercovici and D. Voiculescu, Superconvergence to the central limit and failure of the Cramér theorem for free random variables, Probab. Theory Related Fields 103 (1995), no. 2, 215–222. MR 1355057, DOI 10.1007/BF01204215
- Joachim Cuntz, $K$-theory for certain $C^{\ast }$-algebras, Ann. of Math. (2) 113 (1981), no. 1, 181–197. MR 604046, DOI 10.2307/1971137
- Kenneth J. Dykema, Faithfulness of free product states, J. Funct. Anal. 154 (1998), no. 2, 323–329. MR 1612705, DOI 10.1006/jfan.1997.3207
- —, Purely infinite simple $C^{*}$-algebras arising from free product constructions, II, Math. Scand. (to appear).
- Ken Dykema, Uffe Haagerup, and Mikael Rørdam, The stable rank of some free product $C^*$-algebras, Duke Math. J. 90 (1997), no. 1, 95–121. MR 1478545, DOI 10.1215/S0012-7094-97-09004-9
- Kenneth J. Dykema and Mikael Rørdam, Purely infinite, simple $C^*$-algebras arising from free product constructions, Canad. J. Math. 50 (1998), no. 2, 323–341. MR 1618318, DOI 10.4153/CJM-1998-017-x
- K. J. Dykema and M. Rørdam, Projections in free product $C^*$-algebras, Geom. Funct. Anal. 8 (1998), no. 1, 1–16. MR 1601917, DOI 10.1007/s000390050046
- —, Projections in free product C$\,^{*}$–algebras, II, Math. Z. (to appear).
- Akitaka Kishimoto and Alexander Kumjian, Crossed products of Cuntz algebras by quasi-free automorphisms, Operator algebras and their applications (Waterloo, ON, 1994/1995) Fields Inst. Commun., vol. 13, Amer. Math. Soc., Providence, RI, 1997, pp. 173–192. MR 1424962
- Dan Voiculescu, Symmetries of some reduced free product $C^\ast$-algebras, Operator algebras and their connections with topology and ergodic theory (Buşteni, 1983) Lecture Notes in Math., vol. 1132, Springer, Berlin, 1985, pp. 556–588. MR 799593, DOI 10.1007/BFb0074909
- D. V. Voiculescu, K. J. Dykema, and A. Nica, Free random variables, CRM Monograph Series, vol. 1, American Mathematical Society, Providence, RI, 1992. A noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups. MR 1217253, DOI 10.1090/crmm/001
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
- MR Author ID: 332369
- Email: ken.dykema@math.tamu.edu
- Received by editor(s): December 17, 1998
- Published electronically: May 2, 2000
- Communicated by: David R. Larson
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1707512