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Noncommutative Geometry and Topology in Prague
Free actions of groups on separated graphs and their C*-algebras
Speaker’s name:
Alcides Buss
Speaker’s affiliation:
Federal University of Santa Catarina
Place:
This talk will take place on Zoom:
https://cesnet.zoom.us/j/91975183920?pwd=SGdlRUhLS21HUnVFTXBKcE1vYXlrQT09
Meeting ID: 919 7518 3920
Passcode: 102707
https://cesnet.zoom.us/j/91975183920?pwd=SGdlRUhLS21HUnVFTXBKcE1vYXlrQT09
Meeting ID: 919 7518 3920
Passcode: 102707
Date:
Tuesday, 24. May 2022 - 16:00 to 17:00
Abstract:
In this talk we are consider free actions of a group on a separated graph and explain how this structure reflects on the level of their associated C*-algebras.
We first give a structure theorem for free actions on separated graphs, proving that all those separated graphs are skew products of the group with a certain labeling function to another separated graph, the orbit separated graph. We then explain how to recover the C*-algebra of such separated graphs as a crossed product by a coaction associated to the labeling function. Moreover, we describe the spectral decomposition of those coactions providing in this way a Fell bundle structure for their C*-algebras. All this works for full and reduced C*-algebras of separated graphs.
We first give a structure theorem for free actions on separated graphs, proving that all those separated graphs are skew products of the group with a certain labeling function to another separated graph, the orbit separated graph. We then explain how to recover the C*-algebra of such separated graphs as a crossed product by a coaction associated to the labeling function. Moreover, we describe the spectral decomposition of those coactions providing in this way a Fell bundle structure for their C*-algebras. All this works for full and reduced C*-algebras of separated graphs.