Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-29T19:51:51.598Z Has data issue: false hasContentIssue false
  • English
  • Français

Locating the radical of a triangular operator algebra

Published online by Cambridge University Press:  24 October 2008

Laura Mastrangelo ,
Paul S. Muhly  and
Baruch Solel
Laura Mastrangelo
Affiliation:
Department of Mathematics, University of Puerto Rico, Mayaguez, PR 00681
Paul S. Muhly
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, la 52246
Baruch Solel
Affiliation:
Department of Mathematics, The Technion, 36000 Haifa, Israel
Get access Rights & Permissions [Opens in a new window]

Abstract

Our primary objective is to give necessary and sufficient conditions for a triangular subalgebra of a groupoid C-algebra to be semisimple, i.e. to have vanishing Jacobson radical. If, in addition, the subalgebra is the analytic subalgebra determined by a real-valued cocycle on the groupoid, then we can give an explicit description of the radical in terms of the cocycle. As a consequence of this analysis, we are able to determine when certain analytic crossed products are semisimple.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 115 , Issue 1 , January 1994 , pp. 27 - 38
Copyright
Copyright © Cambridge Philosophical Society 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Birkhoff, G. D.. Dynamical Systems, AMS Colloquium Publications, Vol. 9 (American Mathematical Society, 1927).Google Scholar
[2]Donsig, A. P.. Semisimple triangular AF Algebras. J. Functional Anal., to appear.Google Scholar
[3]Gottschalk, W. H. and Hedlund, G. A.. Topological Dynamics. AMS Colloquium Publications, Vol. 36 (American Mathematical Society, 1955).Google Scholar
[4]Kumjian, A.. On C*-diagonals. Canadian J. Math. 38 (1986), 969–1008.CrossRefGoogle Scholar
[5]Mastrangelo, L.. On radicals of triangular operator algebras. Israel J. Math., to appear.Google Scholar
[6]Muhly, P. S.. Radicals, crossed products, and flows. Ann. Polon. Math. 43 (1983), 35–42.CrossRefGoogle Scholar
[7]Muhly, P., Qru, C. and Solel, B.. Coordinates, nuclearity and spectral subspaces of C*-algebras. J. Operator Theory, to appear.Google Scholar
[8]Muhly, P., Saito, K.-S. and Solel, B.. Coordinates for triangular operator algebras. Ann. Math. 127 (1988), 245–278.CrossRefGoogle Scholar
[9]Muhly, P. and Solel, B.. On triangular subalgebras of groupoid C*-algebras. Israel J. Math. 71 (1990), 257–274.CrossRefGoogle Scholar
[10]Muhley, P. and Williams, D.. Continuous trace groupoid C*-algebras II. Math. Scand. 70 (1992), 127–145.CrossRefGoogle Scholar
[11]Peters, J.. Semi-crossed products of C*-algebras. J. Functional Anal. 59 (1984), 498–534.CrossRefGoogle Scholar
[12]Renault, J. N.. A groupoid approach to C*-algebras. Springer Lecture Notes in Mathematics 793 (Springer Verlag, 1980).CrossRefGoogle Scholar
[13]Solel, B.. Applications of the asymptotic range to analytic subalgebras of groupoid C*-algebras. Ergod. Th. & Dynam. Sys. 12 (1992), 341–358.CrossRefGoogle Scholar
[14]Solel, B. and Ventura, B.. Analytic triangular AF C*-algebras, preprint.Google Scholar