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 (5)

• Tensor Products of Fell Bundles over Groups
• C*-algebras of Toeplitz type associated with algebraic number fields
• Semigroup C*-algebras and amenability of semigroups
• Cuntz-Li relations, Inverse semigroups and Groupoids
• Inverse semigroups and the Cuntz-Li algebras

Cited by in corpus (6)

• On C*-algebras associated to right LCM semigroups
• Nuclearity of semigroup C*-algebras and the connection to amenability
• Nica-Toeplitz algebras associated with product systems over right LCM semigroups
• K-theory for semigroup C*-algebras and partial crossed products
• Co-universality and controlled maps on product systems over right LCM-semigroups
• Independent resolutions for totally disconnected dynamical systems I: Algebraic case