| Title:
|
Weilian prolongations of actions of smooth categories (English) |
| Author:
|
Kolář, Ivan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
133-138 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
First of all, we find some further properties of the characterization of fiber product preserving bundle functors on the category of all fibered manifolds in terms of an infinite sequence $A$ of Weil algebras and a double sequence $H$ of their homomorphisms from [5]. Then we introduce the concept of Weilian prolongation $W_H^A S$ of a smooth category $S$ over ${\mathbb{N}}$ and of its action $D$. We deduce that the functor $(A,H)$ transforms $D$-bundles into $W_H^AD$-bundles. (English) |
| Keyword:
|
Weil bundle |
| Keyword:
|
fiber product preserving bundle functor |
| Keyword:
|
action of smooth category |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 1212.58001 |
| idMR:
|
MR2432850 |
| . |
| Date available:
|
2008-07-24T13:17:57Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116930 |
| . |
| Reference:
|
[1] Doupovec, M., Kolář, I.: Iteration of fiber product preserving bundle functors.Monatsh. Math. 134 (2001), 39–50. Zbl 0999.58001, MR 1872045, 10.1007/s006050170010 |
| Reference:
|
[2] Kolář, I.: Handbook of Global Analysis.ch. Weil Bundles as Generalized Jet Spaces, pp. 625–664, Elsevier, 2008. MR 2389643 |
| Reference:
|
[3] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry.Springer-Verlag, 1993. MR 1202431 |
| Reference:
|
[4] Kolář, I., Mikulski, W. M.: On the fiber product preserving bundle functors.Differential Geom. Appl. 11 (1999), 105–115. MR 1712139, 10.1016/S0926-2245(99)00022-4 |
| Reference:
|
[5] Kolář, I., Mikulski, W. M.: Fiber product preserving bundle functors on all morphisms of fibered manifolds.Arch. Math. (Brno) 42 (2006), 285–293. Zbl 1164.58306, MR 2260388 |
| Reference:
|
[6] Weil, A.: Théorie des points proches sur les variétés différentielles.Colloque de topol. et géom. diff., Strasbourg (1953), 111–117. MR 0061455 |
| . |
