KU-SDU operator algebra seminar (online)
Speaker: Bartosz Kwarsniewski
Title: Stone duality and quasi-orbit spaces for C*-inclusions
Abstract: We consider a C*-subalgebra A of a multiplier algebra of a C*-algebra B. Exploiting the duality between sober spaces and spatial locales, and the adjunction between restriction and induction for ideals in A and B, we identify conditions that allow to define a quasi-orbit space and a quasi-orbit map for the pair (A,B). These objects generalise classical notions for group actions and allow to describe the primitive ideal space of B. Our results are applied to crossed products and cross section C*-algebras of Fell bundles over locally compact groups, regular C*-inclusions, tensor products, relative Cuntz-Pimsner algebras, and crossed products for actions of locally compact Hausdorff groupoids and quantum groups.