C*-crossed products by partial actions and actions of inverse semigroups

Abstract

The recently developed theory of partial actions of discrete groups on $C^{\ast }$-algebras is extended. A related concept of actions of inverse semigroups on $C^{\ast }$-algebras is defined, including covariant representations and crossed products. The main result is that every partial crossed product is a crossed product by a semigroup action.

22 pages, Plain tex

Cited by in corpus (6)

• Nuclearity of semigroup C*-algebras and the connection to amenability
• The dynamics of partial inverse semigroup actions
• The uniform Roe algebra of an inverse semigroup
• Cartan Triples
• Partial Representations and Amenable Fell Bundles over Free Groups
• Partial actions of groups and actions of inverse semigroups