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On the algebra of a free monoid

Published online by Cambridge University Press:  14 November 2011

M. J. Crabb
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, U.K.
C. M. McGregor
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, U.K.
W. D. Munn
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, U.K.
S. Wassermann
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, U.K.

Abstract

Let denote a subring of the complex field that contains 1 and is closed under complex conjugation. It is shown that, with respect to the involution induced by word-reversal, the algebra over of a free monoid admits a trace and a separating family of star matrix representations. From the existence of a trace it is deduced that the aforementioned involution is special, in the sense of Easdown and Munn. Similar results hold for the algebra over of a free monoid with involution.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1996

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References

1Barnes, B. A. and Duncan, J.. The Banach algebra l 1(S). J. of Fund. Anal. 18 (1975), 96113.CrossRefGoogle Scholar
2Cohn, P. M.. Free rings and their relations (London: Academic Press, 1971).Google Scholar
3Crabb, M. J. and Munn, W. D.. Trace functions on the algebras of certain E-unitary inverse semigroups. Proc. Roy. Soc. Edinburgh Sect. A 125 (1995), 10771084.CrossRefGoogle Scholar
4Easdown, D. and Munn, W. D.. On semigroups with involution. Bull. Austral. Math. Soc. 48 (1993), 93100.CrossRefGoogle Scholar
5Easdown, D. and Munn, W. D.. Trace functions on inverse semigroup algebras. Bull. Austral. Math. Soc. 52 (1995), 359372.CrossRefGoogle Scholar
6Goodearl, K. R. and Menal, P.. Free and residually finite-dimensional C*-algebras. J. of Fund. Anal. 90 (1990), 391410.CrossRefGoogle Scholar
7Passman, D. S.. The algebraic theory of group rings (New York: Wiley-Interscience, 1977).Google Scholar
8Petrich, M.. Inverse semigroups (New York: Wiley-Interscience, 1984).Google Scholar