Groupoids, Inverse Semigroups, and their Operator Algebras

• 1. Introduction.- 2. Inverse Semigroups and Locally Compact Groupoids.- 2.1 Inverse semigroups.- 2.2 Locally compact and r-discrete groupoids.- 2.3 Lie groupoids.- 3. Groupoid C*-Algebras and Their Relation to Inverse Semigroup Covariance C*-Algebras.- 3.1 Representation theory for locally compact groupoids.- 3.2 Representation theory for groupoids that are r-discrete, and their inverse semigroups of open G-sets.- 3.3 Groupoid and covariance C*-algebras.- 4. The Groupoid C*-Algebras of Inverse Semigroups.- 4.1 Introduction.- 4.2 Examples of inverse semigroups and their associated groupoids.- 4.3 The universal groupoid of an inverse semigroup.- 4.4 Inverse semigroup universal and reduced C*-algebras as groupoid C*-algebras.- 4.5 Amenability of the von Neumann algebra of an inverse semigroup.- Appendix A. Amenability for Inverse Semigroups.- Appendix B. Groupoid Amenability and Locally Compact Groups.- Appendix C. The Measurability of Fg.- Appendix D. Ind ? as an Induced Representation.- Appendix E. Guichardet’s Disintegration Theorem.- Appendix F. Some Differential Topology.- Index of Terms.- Index of Symbols.

"This outstanding book brings together three mathematical objects 'which a priori seem to have nothing much in common'...The concept of amenability is largely carried over to the present framework. In particular, Clifford semigroups are examined. An example coming from physics, quasicrystals, is discussed. Throughout the monograph explicit clear proofs are provided. The large coverage of this material makes pleasant reading." -Zentralblatt Math