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Title: Linear liftings of skew-symmetric tensor fields to Weil bundles (English)
Author: Dębecki, Jacek
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 55
Issue: 3
Year: 2005
Pages: 809-816
Summary lang: English
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Category: math
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Summary: We define equivariant tensors for every non-negative integer $p$ and every Weil algebra $A$ and establish a one-to-one correspondence between the equivariant tensors and linear natural operators lifting skew-symmetric tensor fields of type $(p,0)$ on an $n$-dimensional manifold $M$ to tensor fields of type $(p,0)$ on $T^AM$ if $1\le p\le n$. Moreover, we determine explicitly the equivariant tensors for the Weil algebras ${\mathbb D}^r_k$, where $k$ and $r$ are non-negative integers. (English)
Keyword: natural operator
Keyword: product preserving bundle functor
Keyword: Weil algebra
MSC: 53A55
MSC: 58A32
idZBL: Zbl 1081.53015
idMR: MR2153104
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Date available: 2009-09-24T11:27:56Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/128024
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Reference: [1] 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
Reference: [2] J.  Grabowski and P.  Urbański: Tangent lifts of Poisson and related structures.J.  Phys.  A 28 (1995), 6743–6777. MR 1381143, 10.1088/0305-4470/28/23/024
Reference: [3] P. Kolář, P.  W.  Michor and J.  Slovák: Natural Operations in Differential Geometry.Springer-Verlag, Berlin, 1993. MR 1202431
Reference: [4] M.  Mikulski: Natural transformations transforming functions and vector fields to functions on some natural bundles.Math. Bohem. 117 (1992), 217–223. Zbl 0810.58004, MR 1165899
Reference: [5] 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
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