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Trace functions on inverse semigroup algebras

Published online by Cambridge University Press:  17 April 2009

D. Easdown  and
W.D. Munn
D. Easdown
Affiliation:
School of Mathematics and StatisticsUniversity of SydneySydneyNew South Wales 2006Australia
W.D. Munn
Affiliation:
Department of MathematicsUniversity of GlasgowGlasgow G12 8QWScotlandUnited Kingdom
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Abstract

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Let S be an inverse semigroup and let F be a subring of the complex field containing 1 and closed under complex conjugation. This paper concerns the existence of trace functions on F[S], the semigroup algebra of S over F. Necessary and sufficient conditions on S are found for the existence of a trace function on F[S] that takes positive integral values on the idempotents of S. Although F[S] does not always admit a trace function, a weaker form of linear functional is shown to exist for all choices of S. This is used to show that the natural involution on F[S] is special. It also leads to the construction of a trace function on F[S] for the case in which F is the real or complex field and S is completely semisimple of a type that includes countable free inverse semigroups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 3 , December 1995 , pp. 359 - 372
Copyright
Copyright © Australian Mathematical Society 1995

References

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