Daniel van Wyk
Studying for Doctor of Philosophy
Area of study:
G.C.R. and C.C.R. groupoid C*-algebras
Supervisors: Astrid an Huef and Lisa Orloff Clark
Previous Degree(s): BSc (Pretoria), BSc Hons (Pretoria), MSc (Pretoria), Postgraduate Certificate in Education (UNISA)
My thesis deals with the classification of groupoid C*-algebras. Groupoid C*-algebras are generalizations of abstract dynamical systems called transformation group C*-algebras. One way to classify C*-algebras is through their representation theory. Two such classifications are called liminal and post-liminal C*-algebras. For transformation group C*-algebras there exist liminal and post-liminal characterizations. For groupoid C*-algebras there are analogous liminal and post-liminal characterizations. At the moment, though, unlike for transformation group C*-algebras, groupoid C*-algebras’ characterizations require an extra assumption, namely amenability. We hypothesize this amenability assumption is redundant. My thesis aims to address this hypothesis.
Abstract dynamical systems, Operator Algebras, Representation theory of groups and groupoids.