Groups and Operator Algebras Seminar

Speaker: Shirly Geffen (University of Münster)

Title: Stable Rank One for Crossed Product C*-Algebras

Abstract: Motivated by the notion of almost finiteness in dynamical systems, as developed by David Kerr, which serves as a key condition for implying Z-stability in the associated crossed product C*-algebra, we investigate dynamical conditions that ensure stable rank one for simple crossed products arising from free dynamical systems. Our results generalize the best-known result by Li and Niu for actions of amenable groups: dynamical systems with the uniform Rokhlin property and comparison of open sets yield stable rank one. Additionally, we establish new results for actions of non-amenable groups. This is ongoing joint work with Jamie Bell and David Kerr.