Equivariant Higher Dixmier-Douady Theory for Circle Actions

Ulrich Pennig (Cardiff University)

Thursday 23rd March, 2023 15:00-16:00 Maths 311B


Continuous fields of operator algebras have found applications in various different areas: among them representation theory, index theory, twisted K-theory and conformal field theory. While the classification of all continuous fields of simple C*-algebras over a topological space is out of reach, section algebras of locally trivial bundles provide a family that is open to classification by methods from homotopy theory. Recently, such bundles also appeared in the classification of group actions on C*-algebras. In joint work Marius Dadarlat and I showed that classical results by Dixmier and Douady generalise to the much larger family of bundles with fibres isomorphic to stabilised strongly self-absorbing C*-algebras. Applications in twisted K-theory revealed interesting examples of equivariant bundles, which motivates the question whether the classification also has an equivariant counterpart. As a starting point for a programme in this direction David Evans and I looked at circle actions on infinite tensor products of matrix algebras and proved that a lot of the theory still carries over. I will report on the progress in this direction.

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