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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
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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

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References

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