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SUMMARY:Noncommutative dynamical systems and crossed products
DTSTART:20231124T130000Z
DTEND:20231124T140000Z
DTSTAMP:20240228T071600Z
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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