Seminarium z Topologii Algebraicznej
Wtorki, 12:15-13:45, sala 4070
15.X.2013
Free actions of compact quantum group on unital C*-algebras
Piotr Hajac
Let F be a field, G a finite group, and Map(G,F) the Hopf algebra of
all set-theoretic maps G -> 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. The main result to be presented in
this talk is an extension of this point of view to arbitrary actions
of compact quantum groups on unital C*-algebras. I will explain that
such an action is free (in the sense of Ellwood) 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 topological group
action on a compact Hausdorff topological space in algebraic terms.
Also, we can apply the main result to noncommutative join
constructions and coactions of discrete groups on unital C*-algebras.
(Joint work with Paul F. Baum and Kenny De Commer.)