Noncommutative Algebra, Analysis and Geometry seminar

A C*-diagonal in the Jiang-Su algebra via entangled matrix cones,  Lukas Obermeyer (University of Münster) 

Abstract: Cartan subalgebras and C*-diagonals in C*-algebras, inspired by Cartan subalgebras in von Neumann algebras, form a bridge between operator algebras and topological dynamics. This connection has led to striking results on the existence of Cartan subalgebras and C*-diagonals in classifiable C*-algebras (and beyond). However, an obstacle to achieving regularity results or progressing toward the long-term goal of classification in certain cases is the lack of explicitly constructed, well-understood examples, even in prominent classifiable C*-algebras such as the Cuntz algebras or the Jiang-Su algebra Z.

In this talk, I will present a new C*-diagonal in Z obtained by an inductive limit construction in which the building blocks are described as entangled matrix cones. This is based on joint work with Wilhelm Winter.