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On the algebra of a free monoid. (English) Zbl 0860.20050
Let \(F\) denote a subring of the complex field that contains 1 and is closed under complex conjugation. First, it is shown that, with respect to the involution induced by word-reversal, the algebra over \(F\) of a free monoid admits a trace and a separating family of star matrix representations and is isomorphic to a subdirect product of a family of matrix algebras; meanwhile, the involution induced by word-reversal is special. Secondly, similar results are obtained for the algebra over \(F\) of a free monoid with involution.
Reviewer: Li Fang (Nanjing)

MSC:
20M25 Semigroup rings, multiplicative semigroups of rings
16S36 Ordinary and skew polynomial rings and semigroup rings
20M05 Free semigroups, generators and relations, word problems
16W10 Rings with involution; Lie, Jordan and other nonassociative structures
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