| Title:
|
On the functorial prolongations of principal bundles (English) |
| Author:
|
Kolář, Ivan |
| Author:
|
Cabras, Antonella |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
719-731 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We describe the fundamental properties of the infinitesimal actions related with functorial prolongations of principal and associated bundles with respect to fiber product preserving bundle functors. Our approach is essentially based on the Weil algebra technique and an original concept of weak principal bundle. (English) |
| Keyword:
|
fiber product preserving bundle functor |
| Keyword:
|
weak principal bundle |
| Keyword:
|
Lie algebroid |
| Keyword:
|
functorial prolongation |
| Keyword:
|
Weil algebra |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| MSC:
|
58H05 |
| idZBL:
|
Zbl 1150.58002 |
| idMR:
|
MR2337425 |
| . |
| Date available:
|
2009-05-05T17:00:50Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119631 |
| . |
| Reference:
|
[1] Bourbaki N.: Groupes et algébres de Lie, I.Hermann, Paris, 1971. MR 0271276 |
| Reference:
|
[2] Cabras A., Kolář I.: Prolongation of tangent valued forms to Weil bundles.Arch. Math. (Brno) 31 (1995), 139-145. MR 1357981 |
| Reference:
|
[3] Doupovec M., Kolář I.: Iteration of fiber product preserving bundle functors.Monatsh. Math. 134 (2001), 39-50. Zbl 0999.58001, MR 1872045 |
| Reference:
|
[4] Ehresmann C.: Les prolongements d'un espace fibré différentiable.CRAS Paris 240 (1955), 1755-1757. Zbl 0064.17502, MR 0071083 |
| Reference:
|
[5] Gancarzewicz J., Mikulski W., Pogoda Z.: Lifts of some tensor fields and connections to product preserving bundles.Nagoya Math. J. 135 (1994), 1-41. MR 1295815 |
| Reference:
|
[6] Kolář I.: Fiber paralelism and connections.Global Differential Geometry and Global Analysis (Berlin, 1979), pp.165-173; Lecture Notes in Mathematics 838, Springer, Berlin-New York, 1981. MR 0636278 |
| Reference:
|
[7] Kolář I.: On the geometry of fiber product preserving bundle functors.Proceedings Conf. Opava 2001, Silesian University, Opava, 2002, pp.85-92. MR 1978765 |
| Reference:
|
[8] Kolář I.: Functorial prolongations of Lie algebroids.Proceedings Conf. Prague 2004, Charles University, Prague, 2005, pp.301-309. MR 2268942 |
| Reference:
|
[9] Kolář, Mikulski W.M.: On the fiber product preserving bundle functors.Differential Geom. Appl. 11 (1999), 105-115. MR 1712139 |
| Reference:
|
[10] Kolář I., Michor P.W., Slovák J.: Natural Operations in Differential Geometry.Springer, Berlin, 1993. MR 1202431 |
| Reference:
|
[11] Mackenzie K.: Lie Groupoids and Lie Algebroids in Differential Geometry.Cambridge University Press, Cambridge, 1987. Zbl 0683.53029, MR 0896907 |
| Reference:
|
[12] Weil A.: Theorie des points proches sur les variétes différentielles.Colloques Internat. CNRS Strasbourg, 1953, pp.111-117. MR 0061455 |
| . |
