Topological construction of C*-correspondences for groupoid C*-algebras

by Rohit Dilip Holkar
Doctoral thesis
Date of Examination:2014-09-12
Date of issue:2015-09-09
Advisor:Prof. Dr. Ralf Meyer
Referee:Prof. Dr. Jean Renault
Referee:Prof. Dr. Thomas Schick
Persistent Address: http://dx.doi.org/10.53846/goediss-5257

 

 

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Abstract

English

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
 
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