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On the contracted l1-algebra of a 0-bisimple inverse semigroup

Published online by Cambridge University Press:  12 July 2007

M. J. Crabb  and
W. D. Munn
M. J. Crabb
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK ([email protected])
W. D. Munn
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK ([email protected])
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Abstract

Let S be a 0-bisimple inverse semigroup and let denote the contracted l1-algebra of S; that is, the Banach algebra l1 (S)/Z, where Z is the ideal spanned by the zero of S. It is shown that, if l1 (G) is primitive for some non-zero maximal subgroup G of S, then is primitive. The same result also holds with primitivity replaced by a stronger condition, here called *-primitivity

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 135 , Issue 2 , April 2005 , pp. 285 - 295
Copyright
Copyright © Royal Society of Edinburgh 2005

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