Deducing properties of graphs from their C*-algebras (and vice versa)

31.01.2024, 13:00  –  Haus 9, Raum 0.17 und Zoom
Forschungsseminar Diskrete Spektraltheorie

Jonathan Taylor (UP)

Abstract: Given a directed row-finite graph, one may define representations of such a graph in C*-algebras and deduce the existence of a unique C*-algebra that is universal for such representations. This C*-algebra is called the graph C*-algebra, or Cuntz-Krieger algebra of the graph. Certain properties of a graph then manifest in particular ways in the associated graph algebra. For example, roughly the better connected a graph is, the fewer closed *-ideals its C*-algebra has (and vice versa). This allows one to analyse a graph or its C*-algebra by analysing the other.
In this talk we shall define the graph C*-algebra of a directed row-finite graph, and describe how one can recover information and properties of the graph from its C*-algebra.