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  • Proceedings of the Edinburgh Mathematical Society, Volume 37, Issue 1
  • February 1994, pp. 119-124

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

  • R. J. Archbold (a1) and J. S. Spielberg (a2)
  • DOI:
  • Published online: 01 January 2009

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.

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1.J. Anderson , Extensions, restrictions, and representations of states on C*-algebras, Trans. Amer. Math. Soc. 249 (1979), 303329.

3.C. J. K. Batty , Simplexes of extensions of states of C*-algebras, Trans Amer. Math. Soc. 272 (1982), 237246.

4.G. A. Elliott , Some simple C*-algebras constructed as crossed products with discrete outer automorphism groups, Publ. Res. Inst. Math. Sci. 16 (1980), 299311.

5.R. V. Kadison and J. R. Ringrose , Derivations and automorphisms of operator algebras, Comm. Math. Phys. 4 (1967), 3263.

6.R. V. Kadison and I. M. Singer , Extensions of pure states, Amer. J. Math. 81 (1959), 383400.

7.S. Kawamura and J. Tomiyama , Properties of topological dynamical systems and corresponding C*-algebras, Tokyo J. Math. 13 (1990), 251257.

8.A. Kishimoto , Outer automorphisms and reduced crossed products of simple C*-algebras, Comm. Math. Phys. 81 (1981), 429435.

10.J. Spielberg , Free-product groups, Cuntz-Krieger algebras, and covariant maps, Internat. J. Math. 2 (1991), 457476.

11.H. Takai , On a duality for crossed products of C*-algebras, J. Funct. Anal. 19 (1975), 2329.

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