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On the algebra of a free monoid

  • M. J. Crabb (a1), C. M. McGregor (a1), W. D. Munn (a1) and S. Wassermann (a1)


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.



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


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