Topological freeness for Hilbert bimodules

Gauge-equivariant Hilbert bimodules and crossed products by endomorphisms

C*-algebra endomorphisms arising from superselection structures with non-trivial centre define a ’rank’ and a ’first Chern class’. Crossed products by such endomorphisms involve the Cuntz-Pimsner algebra of a vector bundle having the above-mentioned rank and first Chern class, and can be used to construct a duality for abstract (nonsymmetric) tensor categories vs. group bundles acting on (nonsy...

Topological Dynamics of Nonstrictly Convex Hilbert Geometries

On Approximation Properties of Pimsner Algebras and Crossed Products by Hilbert Bimodules

Let X be a Hilbert bimodule over a C-algebra A and OX = A ⋊X Z. Using a finite section method we construct a sequence of completely positive contractions factoring through matrix algebras over A which act on sξs ∗ η as Schur multipliers converging to the identity. This shows immediately that for a finitely generated X the algebra OX inherits any standard approximation property such as nuclearit...

A Note on Approximation Properties of Crossed Products by Hilbert Bimodules

Let X be a Hilbert bimodule over a C∗-algebra A and OX = A⋊X Z. Using a finite section method we construct a sequence of completely positive contractions factoring through matrix algebras over A which act on sξs ∗ η as Schur multipliers converging to the identity. This shows immediately that for a finitely generated X the algebra OX inherits any standard approximation property such as nuclearit...

Lecture 11: Soergel Bimodules

In this lecture we continue to study the category O0 and explain some ideas towards the proof of the Kazhdan-Lusztig conjecture. We start by introducing projective functors Pi : O0 → O0 that act by w 7→ w(1 + si) on K0(O0). Using these functors we produce a projective generator of O0. In Section 2 we explain some of the work of Soergel that ultimately was used by Elias and Williamson to give a ...