Mathematics > Operator Algebras
[Submitted on 9 Apr 2013 (this version), latest version 30 Jun 2015 (v4)]
Title:Free actions of compact quantum group on unital C*-algebras
View PDFAbstract: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. In this paper 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 topological group action on a compact Hausdorff topological space in algebraic terms.
Submission history
From: Piotr M. Hajac [view email][v1] Tue, 9 Apr 2013 23:00:19 UTC (13 KB)
[v2] Wed, 12 Feb 2014 19:59:19 UTC (21 KB)
[v3] Sun, 22 Feb 2015 00:19:45 UTC (25 KB)
[v4] Tue, 30 Jun 2015 07:47:57 UTC (25 KB)
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