Local Proof of Algebraic Characterization of Free Actions
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 o...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2014 |
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| Sprache: | English |
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Інститут математики НАН України
2014
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| Zitieren: | 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. |
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Baum, P.F. Hajac, P.M. 2019-02-10T19:06:55Z 2019-02-10T19:06:55Z 2014 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. 1815-0659 2010 Mathematics Subject Classification: 22C05; 55R10; 57S05; 57S10 DOI:10.3842/SIGMA.2014.060 https://nasplib.isofts.kiev.ua/handle/123456789/146694 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Local Proof of Algebraic Characterization of Free Actions Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Local Proof of Algebraic Characterization of Free Actions |
| spellingShingle |
Local Proof of Algebraic Characterization of Free Actions Baum, P.F. Hajac, P.M. |
| title_short |
Local Proof of Algebraic Characterization of Free Actions |
| title_full |
Local Proof of Algebraic Characterization of Free Actions |
| title_fullStr |
Local Proof of Algebraic Characterization of Free Actions |
| title_full_unstemmed |
Local Proof of Algebraic Characterization of Free Actions |
| title_sort |
local proof of algebraic characterization of free actions |
| author |
Baum, P.F. Hajac, P.M. |
| author_facet |
Baum, P.F. Hajac, P.M. |
| publishDate |
2014 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146694 |
| citation_txt |
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. |
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AT baumpf localproofofalgebraiccharacterizationoffreeactions AT hajacpm localproofofalgebraiccharacterizationoffreeactions |
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2025-12-07T20:26:38Z |
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2025-12-07T20:26:38Z |
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1850882599802634240 |