Previous |  Up |  Next


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:
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 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


Files Size Format View
ArchMathRetro_044-2008-2_6.pdf 428.1Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo