Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-28T06:35:30.606Z Has data issue: false hasContentIssue false
  • English
  • Français

Topologically free actions and ideals in discrete C*-dynamical systems

Published online by Cambridge University Press:  20 January 2009

R. J. Archbold  and
J. S. Spielberg
R. J. Archbold
Affiliation:
Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB9 2TY, Scotland
J. S. Spielberg
Affiliation:
Department of Mathematics, Arizona State University, Tempe, AZ85287, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A C*-dynamical system is called topologically free if the action satisfies a certain natural condition weaker than freeness. It is shown that if a discrete system is topologically free then the ideal structure of the crossed product algebra is related to that of the original algebra. One consequence is that a minimal topologically free discrete system has a simple reduced crossed product. Sharper results are obtained when the algebra is abelian.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 37 , Issue 1 , February 1994 , pp. 119 - 124
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

REFERENCES

1.Anderson, J., Extensions, restrictions, and representations of states on C*-algebras, Trans. Amer. Math. Soc. 249 (1979), 303–329.Google Scholar
2.Archbold, R. J., Bunce, J. W. and Gregson, K. D., Extensions of states of C*-algebras, II, Proc. Roy. Soc. Edinburgh 92A (1982), 113–122.Google Scholar
3.Batty, C. J. K., Simplexes of extensions of states of C*-algebras, Trans Amer. Math. Soc. 272 (1982), 237–246.Google Scholar
4.Elliott, G. A., Some simple C*-algebras constructed as crossed products with discrete outer automorphism groups, Publ. Res. Inst. Math. Sci. 16 (1980), 299–311.CrossRefGoogle Scholar
5.Kadison, R. V. and Ringrose, J. R., Derivations and automorphisms of operator algebras, Comm. Math. Phys. 4 (1967), 32–63.CrossRefGoogle Scholar
6.Kadison, R. V. and Singer, I. M., Extensions of pure states, Amer. J. Math. 81 (1959), 383–400.CrossRefGoogle Scholar
7.Kawamura, S. and Tomiyama, J., Properties of topological dynamical systems and corresponding C*-algebras, Tokyo J. Math. 13 (1990), 251–257.CrossRefGoogle Scholar
8.Kishimoto, A., Outer automorphisms and reduced crossed products of simple C*-algebras, Comm. Math. Phys. 81 (1981), 429–435.Google Scholar
9.Quigg, J. C. and Spielberg, J., Regularity and hyporegularity in C*-dynamical system, Houston J. Math. 18 (1992), 139–152.Google Scholar
10.Spielberg, J., Free-product groups, Cuntz-Krieger algebras, and covariant maps, Internat. J. Math. 2 (1991), 457–476.CrossRefGoogle Scholar
11.Takai, H., On a duality for crossed products of C*-algebras, J. Funct. Anal. 19 (1975), 23–29.Google Scholar