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SUMMARY:Equivariant Higher Dixmier-Douady Theory for Circle Actions - Ulri
 ch Pennig (Cardiff University)
DTSTART:20230628T090000Z
DTEND:20230628T100000Z
UID:TALK201985@talks.cam.ac.uk
DESCRIPTION:Continuous fields of operator algebras have found applications
  in various different areas: among them representation theory\, index theo
 ry\, twisted K-theory and conformal field theory. While the classification
  of all continuous fields of simple C*-algebras over a topological space i
 s out of reach\, section algebras of locally trivial bundles provide a fam
 ily that is open to classification by methods from homotopy theory. Recent
 ly\, such bundles also appeared in the classification of group actions on 
 C*-algebras. In joint work Marius Dadarlat and I showed that classical res
 ults 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 equivar
 iant bundles\, which motivates the question whether the classification als
 o has an equivariant counterpart. As a starting point for a programme in t
 his direction David Evans and I looked at circle actions on infinite tenso
 r products of matrix algebras and proved that a lot of the theory still ca
 rries over. I will report on the progress in this direction.
LOCATION:Seminar Room 1\, Newton Institute
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