SEM NCG

[Ludwik Dabrowski]

PIOTR M. HAJAC
(IMPAN / Warsaw University)

"Free actions of compact quantum groups on unital C*-algebras"


Monday 23 July, 11:00-12:30,
SISSA room 136

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Let F be a field, G a finite group, and Map(G,F) the Hopf algebra
of all set-theoretic maps from G to F. If E is a finite field extension
of F and G is its Galois group, the extension is Galois if and only if
the canonical map resulting from viewing E as a Map(G,F)-comodule
is an isomorphism. Similarly, a finite covering space is regular
if and only if the analogous canonical map is an isomorphism.
In this talk, we extend this point of view to actions of compact quantum
groups on unital C*-algebras. We prove that such an action is free
if and only if the canonical map (obtained using the underlying Hopf 
algebra of the compact quantum group) is an isomorphism. In particular,
we are able to express the freeness of a compact Hausdorff group action
on a compact Hausdorff space in algebraic terms.
(Joint work with P. F. Baum and K. De Commer.)