Some liftings of Poisson structures to Weil bundles

Jacek Dębecki

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 2, page 677-687
  • ISSN: 0011-4642

Abstract

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We establish a formula for the Schouten-Nijenhuis bracket of linear liftings of skew-symmetric tensor fields to any Weil bundle. As a result we obtain a construction of some liftings of Poisson structures to Weil bundles.

How to cite

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Dębecki, Jacek. "Some liftings of Poisson structures to Weil bundles." Czechoslovak Mathematical Journal 56.2 (2006): 677-687. <http://eudml.org/doc/31058>.

@article{Dębecki2006,
abstract = {We establish a formula for the Schouten-Nijenhuis bracket of linear liftings of skew-symmetric tensor fields to any Weil bundle. As a result we obtain a construction of some liftings of Poisson structures to Weil bundles.},
author = {Dębecki, Jacek},
journal = {Czechoslovak Mathematical Journal},
keywords = {natural operator; product preserving bundle functor; Weil algebra; Poisson structure; natural operator; product preserving bundle functor; Weil algebra; Poisson structure},
language = {eng},
number = {2},
pages = {677-687},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some liftings of Poisson structures to Weil bundles},
url = {http://eudml.org/doc/31058},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Dębecki, Jacek
TI - Some liftings of Poisson structures to Weil bundles
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 2
SP - 677
EP - 687
AB - We establish a formula for the Schouten-Nijenhuis bracket of linear liftings of skew-symmetric tensor fields to any Weil bundle. As a result we obtain a construction of some liftings of Poisson structures to Weil bundles.
LA - eng
KW - natural operator; product preserving bundle functor; Weil algebra; Poisson structure; natural operator; product preserving bundle functor; Weil algebra; Poisson structure
UR - http://eudml.org/doc/31058
ER -

References

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  7. Jet-like approach to Weil bundles, Seminar Lecture Notes, Masaryk University, Brno, 2001. (2001) 
  8. Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993. (1993) MR1202431
  9. 10.1017/S0027763000002774, Nagoya Math.  J. 109 (1988), 69–89. (1988) Zbl0661.58007MR0931952DOI10.1017/S0027763000002774
  10. The linear natural operators lifting 2 -vector fields to some Weil bundles, Note Mat. 19 (1999), 213–217. (1999) Zbl1008.58004MR1816875
  11. Lectures on the Geometry of Poisson Manifolds, Birkhäuser-Verlag, Basel, 1994. (1994) Zbl0810.53019MR1269545

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