Topological construction of C*-correspondences for groupoid C*-algebras
von Rohit Dilip Holkar
Datum der mündl. Prüfung:2014-09-12
Erschienen:2015-09-09
Betreuer:Prof. Dr. Ralf Meyer
Gutachter:Prof. Dr. Jean Renault
Gutachter:Prof. Dr. Thomas Schick
Dateien
Name:RD-Holkar-Thesis-Math.pdf
Size:1.05Mb
Format:PDF
Description:Doctoral Thesis
Zusammenfassung
Englisch
Let G and H be locally compact, Hausdor groupoids with Haar systems. We de fine a topological correspondence from G to H to be a G-H bispace X carrying a G-quasi invariant and H-invariant family of measures. We show that such a correspondence gives a C*-correspondence from C *(G) to C* (H). If the groupoids and the spaces are second countable, then this construction is functorial. We show that under a certain amenability assumption, similar results hold for the reduced C *-algebras. We apply this theory of correspondences to study induction techniques for groupoid representations, construct morphisms of Brauer groups and produce some odd unbounded KK-cycles.
Keywords: groupoid; topological correspondences; groupoid representation; induced representations; Brauer group; groupoid morphisms; bicategory