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Local Proof of Algebraic Characterization of Free Actions
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Local Proof of Algebraic Characterization of Free Actions
Інший ID:
2010 Mathematics Subject Classification: 22C05; 55R10; 57S05; 57S10
DOI:10.3842/SIGMA.2014.060
DOI:10.3842/SIGMA.2014.060
Посилання:
Local Proof of Algebraic Characterization of Free Actions / P.F. Baum, P.M. Hajac // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 10 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Noncommutative Geometry and Quantum Groups in
honor of Marc A. Rief fel. The full collection is available at http://www.emis.de/journals/SIGMA/Rieffel.html.
We thank the referees for the careful attention they have given to this paper. This work was
partially supported by NCN grant 2011/01/B/ST1/06474. P.F. Baum was partially supported
by NSF grant DMS 0701184.
Дата:
2014
Переглядів:
542
Завантажень:
236
Анотація:
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.
