Given a C*-algebra B, and a regular, abelian, sub-C*-algebra A ⊆ B, we will discuss the opaque ideal Δ ⊴ B, which is a somewhat mysterious ideal that tends to vanish most of the time, but not always. In the last part of the talk I will give an example of a non-vanishing opaque ideal based on an idea of Rufus Willett, and related to the celebrated action of the free group on the 2-sphere used by Banach and Tarski to produce their paradox. This is based on joint work with David Pitts and Vrej Zarikian.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
