INVERSE SEMIGROUP C*-ALGEBRAS ASSOCIATED WITH LEFT CANCELLATIVE SEMIGROUPS

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.