For 2nd-countable effective locally compact Hausdorff etale groupoids, it is known that every nonzero ideal of the reduced C*-algebra has nonzero intersection with the continuous functions on the unit space that vanish at infinity. In this talk, I will discuss an example of Exel using the groupoid of germs construction where this property fails. Showing this involves constructing an example of a special kind of function on the groupoid whose "open" support has empty interior. For any 2nd-countable effective locally compact etale groupoid, a paper of Clark, Exel, Pardo, Sims, and Starling shows that the existence of such an element guarantees that the reduced C*-algebra is not simple.
Our C*-Seminar will still (as it was last year) be on Wednesdays, but the time will now be a bit different: 1:30-2:45 pm (Arizona time, no daylight savings), meeting both in person (WXLR A311) and via zoom.
Also new: it's now the ASUERAU C*-Seminar (so, joint with our friends Lara and Mitch at Embry-Riddle Aeronautical University up the road in Prescott).
(Please email the organizer John Quigg quigg@asu.edu to be put on the email list if you would like to receive the link to the zoom seminar.)
Jeff Long
Arizona State University