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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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1 B. A. Barnes and J. Duncan . The Banach algebra l1(S). J. of Fund. Anal. 18 (1975), 96113.

6 K. R. Goodearl and P. Menal . Free and residually finite-dimensional C*-algebras. J. of Fund. Anal. 90 (1990), 391410.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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