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Compact left ideal groups in semigroup compactification of locally compact groups

Published online by Cambridge University Press:  24 October 2008

J. W. Baker  and
A. T. Lau
J. W. Baker
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, England
A. T. Lau
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, CanadaT6G-261
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Extract

Let G be a locally compact group and let UG denote the spectrum of the C*-algebra LUC(G) of bounded left uniformly continuous complex-valued functions on G, with the Gelfand topology. Then there is a multiplication on UG extending the multiplication on G (when naturally embedded in UG) such that UG is a semigroup and for each x ∈ UG, the map y ↦ yx from UG into UG is continuous, i.e. UG is a compact right topological semigroup. Consequently UG has a unique minimal ideal K which is the union of minimal (closed) left ideals UG. Furthermore K is the union of the set of maximal subgroups of K (see [3], theorem 3·ll).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 3 , May 1993 , pp. 507 - 517
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

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