Hostname: page-component-5c6d5d7d68-wp2c8 Total loading time: 0 Render date: 2024-08-16T06:22:27.434Z Has data issue: false hasContentIssue false
  • English
  • Français

On Inductive Limit Type Actions of the Euclidean Motion Group on Stable UHF Algebras

Published online by Cambridge University Press:  20 November 2018

Andrew J. Dean
Andrew J. Dean*
Affiliation:
Department of Mathematical Sciences, Lakehead University, 955 Oliver Road, Thunder Bay, ON, P7B 5E1 e-mail: andrew.dean@lakeheadu.ca
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.

An invariant is presented which classifies, up to equivariant isomorphism, ${{C}^{*}}$-dynamical systems arising as limits from inductive systems of elementary ${{C}^{*}}$-algebras on which the Euclidean motion group acts by way of unitary representations that decompose into finite direct sums of irreducibles.

Keywords

46L5746L35ClassificationC* -dynamical system
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 2 , 01 June 2006 , pp. 213 - 225
Copyright
Copyright © Canadian Mathematical Society 2006

References

[1] Blackadar, B., K-Theory for Operator Algebras. Mathematical Sciences Research Institute Publications 5, Springer-Verlag, New York, 1986.Google Scholar
[2] Bratteli, O., Elliott, G. A., Evans, D. E., and Kishimoto, A., On the classification of inductive limits of inner actions of a compact group. In: Current Topics in Operator Algebras. World Scientific Publishing, River Edge, NJ, 1991, pp. 13–24.Google Scholar
[3] Dean, A. J., An invariant for actions of ℝ on UHF C*-algebras. C. R. Math. Acad. Sci. R. Can. 23(2001), 91–96.Google Scholar
[4] Dean, A. J., Classification of AF flows. Canadian Math. Bull. 46(2003), 164–177.Google Scholar
[5] Doran, R. S. and Fell, J. M. G., Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles. Volumes I and II. Academic Press, Boston, MA, 1988.Google Scholar
[6] Dixmier, J., C*-Algebras, North-Holland, Amsterdam, 1977.Google Scholar
[7] Elliott, G. A., On the classification of C*-algebras of real rank zero. J. Reine Angew. Math. 443(1993), 179–219.Google Scholar
[8] Elliott, G. A. and Su, H., K-theoretic classification for inductive limit Z 2 actions on AF algebras. Canadian J. Math. 48(1996), 946–958.Google Scholar
[9] Handelman, D. and Rossmann, W., Product type actions of finite and compact groups. Indiana Univ. Math. J. 33(1984), 479–509.Google Scholar
[10] Handelman, D. and Rossmann, W., Actions of compact groups on AF C*-algebras. Illinois J. Math. 29(1985), 51–95.Google Scholar
[11] Kishimoto, A., Actions of finite groups on certain inductive limit C*-algebras. Internat. J. Math. 1(1990), 267–292.Google Scholar
[12] Pedersen, G., C*-Algebras and Their Automorphism Groups. London Mathematical Society Monographs 14, Academic Press, London, 1979.Google Scholar
[13] Pedersen, G., The linear span of projections in simple C*-algebras. J. Operator Theory 4(1980), 289–296.Google Scholar
[14] Sugiura, M., Unitary Representations and Harmonic Analysis. 2nd ed. North-Holland, Amsterdam, 1990.Google Scholar