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 language||English (US)|
|Journal||Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)|
|State||Published - Jun 6 2014|
All Science Journal Classification (ASJC) codes
- Mathematical Physics
- Geometry and Topology