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SUMMARY:Noncommutative dynamical systems and crossed products
DTSTART:20231124T130000Z
DTEND:20231124T140000Z
DTSTAMP:20260612T074900Z
UID:indico-event-10566@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jonathan Taylor\n\nGelfand duality gives the (contra
 variant) equivalence of categories between locally compact Hausdorff (lcH)
  spaces and commutative C*-algebras. An action of a group G on a lcH space
  X induces an action of G on the continuous functions on X via pullback. T
 he analogue for the orbit space X/G is given by the crossed product of C(X
 ) by G\, and *-homomorphisms from this crossed product correspond to repre
 sentations of the dynamical system. The shift to noncommutative dynamics 
 is much easier to phrase in the setting of C*-algebras (rather than topolo
 gical spaces)\, and one may still construct crossed products by group acti
 ons. A new question arises: what is the correct notion of a `non-trivial' 
 action on a C*-algebra? Going further\, what properties of the inclusion o
 f the algebra C(X) into the crossed product generalise to the noncommutati
 ve setting? The aim of this talk is to introduce noncommutative dynamical 
 systems and show how certain properties in the classical setting generalis
 e. Time permitting\, we shall discuss some of the convenient properties of
  sufficiently `non-trivial' NC dynamical systems and their crossed product
 s.\n\nhttps://indico.math.cnrs.fr/event/10566/
LOCATION:Fokko du Cloux (Bâtiment Braconnier)
URL:https://indico.math.cnrs.fr/event/10566/
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