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Linear liftings of skew-symmetric tensor fields to Weil bundles
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 3, pp. 809-816
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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.
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.
Classification : 53A55, 58A32
Keywords: natural operator; product preserving bundle functor; Weil algebra 
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     title = {Linear liftings of skew-symmetric tensor fields to {Weil} bundles},
     journal = {Czechoslovak Mathematical Journal},
     pages = {809--816},
     year = {2005},
     volume = {55},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2005_55_3_a21/}
}
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Dębecki, Jacek. Linear liftings of skew-symmetric tensor fields to Weil bundles. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 3, pp. 809-816. http://geodesic.mathdoc.fr/item/CMJ_2005_55_3_a21/

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