Operator Algebras And Dynamics: Groupoids, Crossed Products, And Rokhlin Dimension (advanced Courses In Mathematics - Crm Barcelona)

This book collects the notes of the lectures given at the Advanced Course on Crossed Products, Groupoids, and Rokhlin dimension, that took place at the Centre de Recerca Matemàtica (CRM) from March 13 to March 17, 2017. The notes consist of three series of lectures. The first one was given by Dana Williams (Dartmouth College), and served as an introduction to crossed products of C\*-algebras and the study of their structure. The second series of lectures was delivered by Aidan Sims (Wollongong), who gave an overview of the theory of topological groupoids (as a model for groups and group actions) and groupoid C\*-algebras, with particular emphasis on the case of étale groupoids. Finally, the last series was delivered by Gábor Szabó (Copenhagen), and consisted of an introduction to Rokhlin type properties (mostly centered around the work of Hirshberg, Winter and Zacharias) with hints to the more advanced theory related to groupoids. Front Matter ....Pages i-x Front Matter ....Pages 1-4 What is a Crossed Product? (Aidan Sims, Gábor Szabó, Dana Williams)....Pages 5-16 Induced Representations and Imprimitivity Theorems (Aidan Sims, Gábor Szabó, Dana Williams)....Pages 17-27 Ideal Structure (Aidan Sims, Gábor Szabó, Dana Williams)....Pages 29-36 Type Theory, Actions on the Compacts and the Effros–Hahn Theory (Aidan Sims, Gábor Szabó, Dana Williams)....Pages 37-44 Tensor Products, K-Theory and Rotation Algebras (Aidan Sims, Gábor Szabó, Dana Williams)....Pages 45-52 The Roads Not Taken (Aidan Sims, Gábor Szabó, Dana Williams)....Pages 53-57 Front Matter ....Pages 59-61 Introduction (Aidan Sims, Gábor Szabó, Dana Williams)....Pages 63-66 Etale Groupoids (Aidan Sims, Gábor Szabó, Dana Williams)....Pages 67-76 C*-algebras and Equivalence (Aidan Sims, Gábor Szabó, Dana Williams)....Pages 77-88 Fundamental Structure Theory (Aidan Sims, Gábor Szabó, Dana Williams)....Pages 89-102 Cartan Pairs, and Dixmier–Douady Theory for Fell Algebras (Aidan Sims, Gábor Szabó, Dana Williams)....Pages 103-120 Front Matter ....Pages 121-123 Introduction (Aidan Sims, Gábor Szabó, Dana Williams)....Pages 125-127 Classical Dynamical Systems (Aidan Sims, Gábor Szabó, Dana Williams)....Pages 129-135 Classification Theory and Nuclear Dimension (Aidan Sims, Gábor Szabó, Dana Williams)....Pages 137-140 Rokhlin Dimension for Finite Groups (Aidan Sims, Gábor Szabó, Dana Williams)....Pages 141-145 Single Automorphisms (Aidan Sims, Gábor Szabó, Dana Williams)....Pages 147-153 Outlook: Generalizations (Aidan Sims, Gábor Szabó, Dana Williams)....Pages 155-161 Back Matter ....Pages 163-163 This book collects the notes of the lectures given at the Advanced Course on Crossed Products, Groupoids, and Rokhlin dimension, that took place at the Centre de Recerca Matematica (CRM) from March 13 to March 17, 2017.