On the functorial prolongations of principal bundles

Ivan Kolář; Antonella Cabras

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 4, page 719-731
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Kolář, Ivan, and Cabras, Antonella. "On the functorial prolongations of principal bundles." Commentationes Mathematicae Universitatis Carolinae 47.4 (2006): 719-731. <http://eudml.org/doc/249846>.

@article{Kolář2006,
abstract = {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.},
author = {Kolář, Ivan, Cabras, Antonella},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {fiber product preserving bundle functor; weak principal bundle; Lie algebroid; functorial prolongation; Weil algebra; weak principal bundle},
language = {eng},
number = {4},
pages = {719-731},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the functorial prolongations of principal bundles},
url = {http://eudml.org/doc/249846},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Kolář, Ivan
AU - Cabras, Antonella
TI - On the functorial prolongations of principal bundles
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 4
SP - 719
EP - 731
AB - 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.
LA - eng
KW - fiber product preserving bundle functor; weak principal bundle; Lie algebroid; functorial prolongation; Weil algebra; weak principal bundle
UR - http://eudml.org/doc/249846
ER -

References

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  1. Bourbaki N., Groupes et algébres de Lie, I, Hermann, Paris, 1971. MR0271276
  2. Cabras A., Kolář I., Prolongation of tangent valued forms to Weil bundles, Arch. Math. (Brno) 31 (1995), 139-145. (1995) MR1357981
  3. Doupovec M., Kolář I., Iteration of fiber product preserving bundle functors, Monatsh. Math. 134 (2001), 39-50. (2001) Zbl0999.58001MR1872045
  4. Ehresmann C., Les prolongements d'un espace fibré différentiable, CRAS Paris 240 (1955), 1755-1757. (1955) Zbl0064.17502MR0071083
  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. (1994) MR1295815
  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. MR0636278
  7. Kolář I., On the geometry of fiber product preserving bundle functors, Proceedings Conf. Opava 2001, Silesian University, Opava, 2002, pp.85-92. MR1978765
  8. Kolář I., Functorial prolongations of Lie algebroids, Proceedings Conf. Prague 2004, Charles University, Prague, 2005, pp.301-309. MR2268942
  9. Kolář, Mikulski W.M., On the fiber product preserving bundle functors, Differential Geom. Appl. 11 (1999), 105-115. (1999) MR1712139
  10. Kolář I., Michor P.W., Slovák J., Natural Operations in Differential Geometry, Springer, Berlin, 1993. MR1202431
  11. Mackenzie K., Lie Groupoids and Lie Algebroids in Differential Geometry, Cambridge University Press, Cambridge, 1987. Zbl0683.53029MR0896907
  12. Weil A., Theorie des points proches sur les variétes différentielles, Colloques Internat. CNRS Strasbourg, 1953, pp.111-117. MR0061455

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