Equivariant dimensions on graph C*-algebras (P2)

Graph C*-algebras are universal C*-algebras associated with directed graphs that generalize Cuntz--Krieger algebras. Many examples of C*-algebras turn out to be graph C*-algebras, e.g. matrix algebras, the Toeplitz algebra, the Cuntz algebras, the C*-algebra of compact operators on a separable Hilbert space, q-deformed spheres, q-deformed projective spaces, q-deformed lens spaces. The advantage of this class of C*-algebras is that many of their properties, like simplicity or classification of certain ideals, can be described purely in terms of the underlying graph. There is a natural U(1)-action, called the gauge action, on every graph C*-algebra. In my talk, I will concentrate on this action and its restriction to finite subgroups from the perspective of the recently introduced local-triviality dimension of the action. I will illustrate all results in particular examples.