Hannes Thiel (Chalmers University & University of Gothenburg)
15:30-16:30,July 31th,2024
Shanghai Institute for Mathematics and Interdisciplinary Sciences
Abstract:
In his seminal investigation of Z-stability for simple, nuclear C*-algebras, Winter introduced the notion of (m,n)-pureness with m and n quantifying comparison and divisibility properties in the Cuntz semigroup, and he showed that every simple C*-algebra that has locally finite nuclear dimension and that is (m,n)-pure for some m and n is Z-stable. Combined with the result of Roerdam that every Z-stable C*-algebra is pure (that is, (0,0)-pure, which means that its Cuntz semigroup has the strongest comparison and divisibility properties), this provides a situation where (m,n)-pureness implies pureness. In a recent paper with R. Antoine, F. Perera and L. Robert, we removed the assumption of locally finite nuclear dimension and showed that every simple, (m,n)-pure C*-algebra is pure. In this work we generalize the result even further by showing that (m,n)-pureness implies pureness in general. As an application we show that every C*-algebra with the Global Glimm Property and finite nuclear dimension is pure. This is joint work with R. Antoine, F. Perera, and E. Vilalta.
About the speaker:
Hannes Thiel is a Professor at the Department of Mathematical Sciences at the Chalmers University of Technology and University of Gothenburg. Since 2023 he is a Wallenberg Academy Fellow. Professor Thiel’s research interests involve operator algebras and abstract harmonic analysis. He has published in top-tier mathematical journals such as the Journal of Functional Analysis, Advances in Mathematics, and Duke Mathematical Journal.