| Title:
|
Some liftings of Poisson structures to Weil bundles (English) |
| Author:
|
Dębecki, Jacek |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
677-687 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
natural operator |
| Keyword:
|
product preserving bundle functor |
| Keyword:
|
Weil algebra |
| Keyword:
|
Poisson structure |
| MSC:
|
53D17 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 1164.58308 |
| idMR:
|
MR2291766 |
| . |
| Date available:
|
2009-09-24T11:36:51Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128096 |
| . |
| Reference:
|
[1] J. Dębecki: Linear liftings of skew-symmetric tensor fields to Weil bundles.Czechoslovak Math. J 55(130) (2005), 809-816. MR 2153104, 10.1007/s10587-005-0067-0 |
| Reference:
|
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| Reference:
|
[3] J. Gancarzewicz, W. Mikulski, and Z. Pogoda: Lifts of some tensor fields and connections to product preserving functors.Nagoya Math. J. 135 (1994), 1–41. MR 1295815, 10.1017/S0027763000004931 |
| Reference:
|
[4] J. Grabowski, P. Urbański: Tangent lifts of Poisson and related structures.J. Phys. A, Math. Gen. 28 (1995), 6743–6777. MR 1381143, 10.1088/0305-4470/28/23/024 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[7] I. Kolář: Jet-like approach to Weil bundles.Seminar Lecture Notes, Masaryk University, Brno, 2001. |
| Reference:
|
[8] I. Kolář, P. W. Michor, J. Slovák: Natural Operations in Differential Geometry.Springer-Verlag, Berlin, 1993. MR 1202431 |
| Reference:
|
[9] O. O. Luciano: Categories of multiplicative functors and Weil’s infinitely near points.Nagoya Math. J. 109 (1988), 69–89. Zbl 0661.58007, MR 0931952, 10.1017/S0027763000002774 |
| Reference:
|
[10] W. M. Mikulski: The linear natural operators lifting $2$-vector fields to some Weil bundles.Note Mat. 19 (1999), 213–217. Zbl 1008.58004, MR 1816875 |
| Reference:
|
[11] I. Vaisman: Lectures on the Geometry of Poisson Manifolds.Birkhäuser-Verlag, Basel, 1994. Zbl 0810.53019, MR 1269545 |
| . |
