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C*-algebras of Clifford semigroups

Published online by Cambridge University Press:  14 November 2011

John Duncan  and
A.L.T. Paterson
John Duncan
Affiliation:
Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR 72701, U.S.A.
A.L.T. Paterson
Affiliation:
Department of Mathematics, University of Aberdeen, Aberdeen AB9 2TY, Scotland, U.K.
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Synopsis

We investigate algebras associated with a (discrete) Clifford semigroup S =∪ {Ge: e ∈ E{. We show that the representation theory for S is determined by an enveloping Clifford semigroup UC(S) =∪ {Gx: x ∈ X} where X is the filter completion of the semilattice E. We describe the representation theory in terms of both disintegration theory and sheaf theory.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 111 , Issue 1-2 , 1989 , pp. 129 - 145
Copyright
Copyright © Royal Society of Edinburgh 1989

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