This article should be considered as a continuation of the work started by the first named author in [3], where the notion of tight representations of inverse semigroups was introduced and used to study a large class of C*-algebras. Given any inverse semigroup S, the theory developed in [3] gives a recipe to build an étale groupoid, denoted Gtight(S), whose C*-algebra is isomorphic to the universal C*-algebra for tight representations of S. Since then a very large number of C*-algebras were… CONTINUE READING