Geodesic
Representations of the l1-algebra of an inverse semigroup having the separation property†
Glasgow mathematical journal, Tome 18 (1977) no. 2, pp. 131-143

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Let S be a semigroup, and let l1(S) denote the l1-semigroup algebra of S. Beginning with the fundamental paper of E. Hewitt and H. Zuckerman [5], there has been a considerable amount of research done concerning the Banach algebra l1(S) in the case when S is abelian; see the bibliography [7]. However, until recently, there was very little information known concerning l1(S) when S was nonabelian and infinite. Now for certain classes of infinite nonabelian semigroups with involution, recent progress has been made in the study of the Banach *-algebra l1(S) and the *-representations of l1(S). In [2], B. Barnes and J. Duncan prove that l1(S) is Jacobson semisimple, study the spectrum of elements in l1(S), and construct and study *-representations of l1(S) when S is the free semigroup with a finite or countably infinite set of generators (and also in some cases where the generators satisfy certain relations). In [1], the present author considered the representation theory of l1(S) where S is an inverse semigroup. This paper is a sequel to [1]. 
Barnes, Bruce A. Representations of the l1-algebra of an inverse semigroup having the separation property†. Glasgow mathematical journal, Tome 18 (1977) no. 2, pp. 131-143. doi: 10.1017/S0017089500003177
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