Inverse semigroup C*-algebras associated with left cancellative semigroups

摘要

To each discrete left cancellative semigroup $S$ one may associate a certaininverse semigroup $I_l(S)$, often called the left inverse hull of $S$. We showhow the full and the reduced C*-algebras of $I_l(S)$ are related to the fulland reduced semigroup C*-algebras for $S$ recently introduced by Xin Li, andgive conditions ensuring that these algebras are isomorphic. Our pictureprovides an enhanced understanding of Li's algebras.