Locally trivial W*-bundles

Classification of operator algebras: complexity, rigidity, and dynamics

04 February 14:00 - 15:00

Ulrich Pennig - Westfälische Wilhelms-Universität Münster

Tracially continuous W*-bundles were introduced by Ozawa. Their study was motivated by work on the structure and classification of simple, nuclear C*-algebras. They are similar in spirit to C(X)-algebras. Their fibres, however, are tracial von Neumann algebras. In joint work with Sam Evington, we prove that a tracially continuous W*-bundle over a compact Hausdorff space with all fibres isomorphic to the hyperfinite type II1-factor R that is locally trivial already has to be globally trivial. The proof uses the contractibility of the automorphism group Aut(R) shown by Popa and Takesaki. There is no restriction on the covering dimension of the underlying space.
Marius Dadarlat
Purdue University
Søren Eilers
University of Copenhagen
Asger Törnquist
University of Copenhagen


Søren Eilers


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