BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ralf Meyer DTSTART:20200930T120000Z DTEND:20200930T133000Z DTSTAMP:20260423T052335Z UID:WSIPM/2 DESCRIPTION:Title: Gr oupoid models and C*-algebras of diagrams of groupoid correspondences\ nby Ralf Meyer as part of Western Sydney\, IPM joint workshop on Operator Algebras\n\n\nAbstract\nA groupoid correspondence is a generalised morphi sm between étale groupoids. Topological graphs\, self-similarities of gr oups\, or self-similar graphs are examples of this. Groupoid corresponden ces induce C*-correspondences between groupoid C*-algebras\, which then gi ve Cuntz-Pimsner algebras. The Cuntz-Pimsner algebra of a groupoid corres pondence is isomorphic to a groupoid C*-algebra of an étale groupoid buil t from the groupoid correspondence. This gives a uniform construction of groupoid models for many interesting C*-algebras\, such as graph C*-algebr as of regular graphs\, Nekrashevych's C*-algebras of self-similar groups a nd their generalisation by Exel and Pardo for self-similar graphs. If pos sible\, I would also like to mention work in progress to extend this theor em to relative Cuntz-Pimsner algebras\, which would then cover all topolog ical graph C*-algebras.\nGroupoid correspondences form a bicategory. This structure is already used to form the groupoid model of a groupoid corres pondence. It also allows us to define actions of monoids or\, more genera lly\, of categories on groupoids by groupoid correspondences. Passing to C*-algebras\, this gives a product system where the unit fibre is a groupo id C*-algebra. If the monoid is an Ore monoid\, then the Cuntz-Pimsner al gebra of this product system is again a groupoid C*-algebra of an étale g roupoid\, which is defined directly from the action by groupoid correspond ences. For more general monoids\, the two constructions become different\ , however. We show this in a special case that is related to separated gr aph C*-algebras and their tame versions.\n LOCATION:https://researchseminars.org/talk/WSIPM/2/ END:VEVENT END:VCALENDAR