Duke Mathematical Journal

Finite group actions on C*-algebras with the Rohlin property, I

Masaki Izumi

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Abstract

Basic properties of finite group actions with the Rohlin property on unital C*-algebras are investigated. A characterization of finite group actions with the Rohlin property on the Cuntz algebra $\mathcal{O}_2$ is given in terms of central sequences, which may be considered as an equivariant version of E. Kirchberg and N. C. Phillips's characterization of $\mathcal{O}_2$. A large class of symmetries on $\mathcal{O}_2$ are classified in terms of the fixed-point algebras for conjugacy and the crossed products for cocycle conjugacy. Model actions of symmetries of $\mathcal{O}_2$ are constructed for given K-theoretical invariants.

Article information

Source
Duke Math. J. Volume 122, Number 2 (2004), 233-280.

Dates
First available: 14 April 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1081971768

Digital Object Identifier
doi:10.1215/S0012-7094-04-12221-3

Mathematical Reviews number (MathSciNet)
MR2053753

Zentralblatt MATH identifier
1050.46049

Subjects
Primary: 46L40: Automorphisms 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]
Secondary: 46L35: Classifications of $C^*$-algebras 46L80: $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]

Citation

Izumi, Masaki. Finite group actions on C * -algebras with the Rohlin property, I. Duke Mathematical Journal 122 (2004), no. 2, 233--280. doi:10.1215/S0012-7094-04-12221-3. http://projecteuclid.org/euclid.dmj/1081971768.


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