Weilian prolongations of actions of smooth categories
Archivum Mathematicum (2008)
- Volume: 044, Issue: 2, page 133-138
- ISSN: 0044-8753
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topKolář, Ivan. "Weilian prolongations of actions of smooth categories." Archivum Mathematicum 044.2 (2008): 133-138. <http://eudml.org/doc/250436>.
@article{Kolář2008,
abstract = {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.},
author = {Kolář, Ivan},
journal = {Archivum Mathematicum},
keywords = {Weil bundle; fiber product preserving bundle functor; action of smooth category; Weil bundle; fiber product preserving bundle functor; action of smooth category},
language = {eng},
number = {2},
pages = {133-138},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Weilian prolongations of actions of smooth categories},
url = {http://eudml.org/doc/250436},
volume = {044},
year = {2008},
}
TY - JOUR
AU - Kolář, Ivan
TI - Weilian prolongations of actions of smooth categories
JO - Archivum Mathematicum
PY - 2008
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 044
IS - 2
SP - 133
EP - 138
AB - 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.
LA - eng
KW - Weil bundle; fiber product preserving bundle functor; action of smooth category; Weil bundle; fiber product preserving bundle functor; action of smooth category
UR - http://eudml.org/doc/250436
ER -
References
top- Doupovec, M., Kolář, I., 10.1007/s006050170010, Monatsh. Math. 134 (2001), 39–50. (2001) Zbl0999.58001MR1872045DOI10.1007/s006050170010
- Kolář, I., Handbook of Global Analysis, ch. Weil Bundles as Generalized Jet Spaces, pp. 625–664, Elsevier, 2008. (2008) MR2389643
- Kolář, I., Michor, P. W., Slovák, J., Natural Operations in Differential Geometry, Springer-Verlag, 1993. (1993) MR1202431
- Kolář, I., Mikulski, W. M., 10.1016/S0926-2245(99)00022-4, Differential Geom. Appl. 11 (1999), 105–115. (1999) MR1712139DOI10.1016/S0926-2245(99)00022-4
- Kolář, I., Mikulski, W. M., Fiber product preserving bundle functors on all morphisms of fibered manifolds, Arch. Math. (Brno) 42 (2006), 285–293. (2006) Zbl1164.58306MR2260388
- Weil, A., Théorie des points proches sur les variétés différentielles, Colloque de topol. et géom. diff., Strasbourg (1953), 111–117. (1953) MR0061455
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