Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

On the algebra of a free monoid

M. J. Crabba1, C. M. McGregora1, W. D. Munna1 and S. Wassermanna1

a1 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.

(Received March 28 1995)