Inverse Semigroup<i>C</i>*-Algebras Associated with Left Cancellative Semigroups

Abstract

Abstract To each discrete left cancellative semigroup S one may associate an inverse semigroup I l (S) , often called the left inverse hull of S . We show how the full and reduced C *-algebras of I l (S) are related to the full and reduced semigroup C *-algebras for S , recently introduced by Li, and give conditions ensuring that these algebras are isomorphic. Our picture provides an enhanced understanding of Li's algebras.