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:
| Datum: | 2014 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2014
|
| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.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| id |
irk-123456789-146694 |
|---|---|
| record_format |
dspace |
| fulltext |
|
| spelling |
irk-123456789-1466942019-02-12T01:25:02Z Local Proof of Algebraic Characterization of Free Actions Baum, P.F. Hajac, P.M. 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. 2014 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146694 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Baum, P.F. Hajac, P.M. |
| spellingShingle |
Baum, P.F. Hajac, P.M. Local Proof of Algebraic Characterization of Free Actions Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Baum, P.F. Hajac, P.M. |
| author_sort |
Baum, P.F. |
| title |
Local Proof of Algebraic Characterization of Free Actions |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT baumpf localproofofalgebraiccharacterizationoffreeactions AT hajacpm localproofofalgebraiccharacterizationoffreeactions |
| first_indexed |
2025-07-11T00:26:29Z |
| last_indexed |
2025-07-11T00:26:29Z |
| _version_ |
1837308145823645696 |