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ALGEBRAS ASSOCIATED WITH A FREE INVERSE MONOID

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  01 February 2009

M. J. CRABB
M. J. CRABB*
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, UK (email: [email protected])
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Abstract

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Let S be an ideal of the free inverse monoid on a set X, and let ℬ denote the Banach algebra l1(S). It is shown that the following statements are equivalent: ℬ is *-primitive; ℬ is prime; X is infinite. A similar result holds if ℬ is replaced by ℂ[S], the complex semigroup algebra of S.

Keywords

primitivitysemigroup algebra

MSC classification

Secondary: 43A20: $L^1$-algebras on groups, semigroups, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 1 , February 2009 , pp. 27 - 31
Copyright
Copyright © Australian Mathematical Society 2009

References

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[3]Duncan, J., ‘Dual representations of Banach algebras’, PhD Thesis, University of Newcastle-upon-Tyne, 1964.Google Scholar
[4]Lawson, M. V., Inverse Semigroups (World Scientific, Singapore, 1998).CrossRefGoogle Scholar
[5]McGregor, C. M., ‘A representation for l 1(S)’, Bull. London Math. Soc. 8 (1976), 156–160.CrossRefGoogle Scholar