Representations of the 𝑙¹-algebra of an inverse semigroup

Abstract

In this paper the star representations on Hilbert space of the l 1 {l^1} -algebra of an inverse semigroup are studied. It is shown that the set of all irreducible star representations form a separating family for the l 1 {l^1} -algebra. Then specific examples of star representations are constructed, and some theory of star representations is developed for the l 1 {l^1} -algebra of a number of the most important examples of inverse semigroups.