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...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2014 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2014
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146694 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862742655430033408 |
|---|---|
| author | Baum, P.F. Hajac, P.M. |
| author_facet | Baum, P.F. Hajac, P.M. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
|
| first_indexed | 2025-12-07T20:26:38Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146694 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:26:38Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Local Proof of Algebraic Characterization of Free Actions Baum, P.F. Hajac, P.M. |
| title | 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_short | Local Proof of Algebraic Characterization of Free Actions |
| title_sort | local proof of algebraic characterization of free actions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146694 |
| work_keys_str_mv | AT baumpf localproofofalgebraiccharacterizationoffreeactions AT hajacpm localproofofalgebraiccharacterizationoffreeactions |