Local proof of algebraic characterization of free actions

Paul F. Baum, Piotr M. Hajac

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Let G be a compact Hausdorff topological group acting on a compact Hausdorff topological space X. Within the C*-algebra C(X) of all continuous complex-valued functions on X, there is the Peter-Weyl algebra PG(X) which is the (purely algebraic) direct sum of the isotypical components for the action of G on C(X). We prove that the action of G on X is free if and only if the canonical map PG(X)⊗C(X/G)PG(X)→PG(X)⊗O(G) is bijective. Here both tensor products are purely algebraic, and O(G) denotes the Hopf algebra of "polynomial" functions on G.

Original languageEnglish (US)
Article number060
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume10
DOIs
StatePublished - Jun 6 2014

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

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