Inverse semigroup C*-algebras associated with left cancellative semigroups

Abstract

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

31 pages

References in corpus (1)

• Inverse semigroups and the Cuntz-Li algebras

Cited by in corpus (1)

• Nuclearity of semigroup C*-algebras and the connection to amenability