The Groupoid C*-Algebras of Inverse Semigroups
Alan L. T. Paterson · Birkhäuser Boston eBooks · 1999
In Chapter 3, we investigated the relationship between r-discrete groupoids and inverse semigroup actions (in the form of localizations ( X, S )). We showed in particular (Theorem 3.3.1) that for every r-discrete groupoid G , there is an inverse subsemigroup S of G op such that C* ( G ) is isomorphic to the covariance algebra C 0 ( G 0 ) × β S . Conversely, under reasonable conditions, covariance C *-algebras are r-discrete groupoid C *-algebras (Corollary 3.3.2). So r-discrete groupoids are essentially the same as localizations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.