Operator Algebra Seminar

Abstrakt finns enbart på engelska: I will introduce type semigroups for twisted groupoids which are a dynamical version of Cuntz semigroups. The type semigroup encodes information about traces and ideals in the reduced groupoid C*-algebra, making it easy to detect pure infiniteness and stable finiteness. If the reduced C*-algebra of the twisted groupoid is simple and the type semigroup satisfies a weak version of almost unperforation, then the C*-algebra is either purely infinite or stably finite. I will show another advantage of type semigroups for transformation groupoids in that they encode information about dynamical comparison in the form of almost unperforation, allowing us to apply the dichotomy result to dynamical systems. Part of this talk is based on joint work with B. Kwaśniewski, H. Thiel and J. Wu.