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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)

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.

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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.
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