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A class of groups producing simple, unique trace C*-algebras

Published online by Cambridge University Press:  24 October 2008

S. David Promislow
Affiliation:
Department of Mathematics and Statistics, York University, 4700 Keele St, North York, ON, CanadaM3J 1P3

Abstract

We define and study a class of groups which produce simple, unique trace, C*-algebras. This class strictly contains the class of weak Powers groups, as shown by the fact that it is closed under extensions. We provide answers to some open problems involving Powers and weak Powers groups.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

REFERENCES

[1]Akemann, C. A. and Lee, T. Y.. Some simple C*-algebras associated with free groups. Indiana Math. J. 29 (1980), 505511.CrossRefGoogle Scholar
[2]Akemann, C. A. and Ostrand, P.. Computing norms in group C*-algebras. Amer. J. Math. 98 (1976), 10151047.CrossRefGoogle Scholar
[3]Bedos, E.. Discrete groups and simple C*-algebras. Math. Proc. Cambridge Philos. Soc. 109 (1991), 521537.CrossRefGoogle Scholar
[4]Bocca, F. and Nitica, V.. Combinatorial properties of groups and simple C*-algebras with a unique trace. J. Operator Theory 20 (1988), 183196.Google Scholar
[5]de la Harpe, P.. Reduced C*-algebras of discrete groups which are simple with a unique trace. Lecture Notes in Mathematics, 1132 (Springer-Verlag, 1985), 230253.Google Scholar
[6]Kesten, H.. Symmetric random walks on groups. Trans. American Math. Soc. 92 (1959), 336354.CrossRefGoogle Scholar
[7]Lyndon, R. C. and Schupp, P. E.. Combinatorial Group Theory (Springer, 1977).Google Scholar
[8]Magnus, W., Karrass, A. and Solitar, D.. Combinatorial Group Theory (Interscience, 1966).Google Scholar
[9]Paschke, W. L. and Salinas, N.. C*-algebras associated with free products of groups. Pacific J. Math. 82 (1979), 211221.CrossRefGoogle Scholar
[10]Powers, R. T.. Simplicity of the C*-algebra associated with the free group on two generators. Duke Math. J. 42 (1975), 151156.CrossRefGoogle Scholar