Seminar series
Date
Tue, 16 Jul 2024
Time
16:00 -
17:00
Location
C4
Speaker
Andrew Toms
Organisation
Purdue University
The Cuntz semigroup of a C*-algebra is an ordered monoid consisting of equivalence classes of positive elements in the stabilization of the algebra. It can be thought of as a generalization of the Murray-von Neumann semigroup, and records substantial information about the structure of the algebra. Here we examine the set of positive elements having a fixed equivalence class in the Cuntz semigroup of a simple, separable, exact and Z-stable C*-algebra and show that this set is path connected when the class is non-compact, i.e., does not correspond to the class of a projection in the C*-algebra. This generalizes a known result from the setting of real rank zero C*-algebras.