# Linear natural operators lifting $p$-vectors to tensors of type $(q,0)$ on Weil bundles

Czechoslovak Mathematical Journal (2016)

- Volume: 66, Issue: 2, page 511-525
- ISSN: 0011-4642

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topDębecki, Jacek. "Linear natural operators lifting $p$-vectors to tensors of type $(q,0)$ on Weil bundles." Czechoslovak Mathematical Journal 66.2 (2016): 511-525. <http://eudml.org/doc/280099>.

@article{Dębecki2016,

abstract = {We give a classification of all linear natural operators transforming $p$-vectors (i.e., skew-symmetric tensor fields of type $(p,0)$) on $n$-dimensional manifolds $M$ to tensor fields of type $(q,0)$ on $T^AM$, where $T^A$ is a Weil bundle, under the condition that $p\ge 1$, $n\ge p$ and $n\ge q$. The main result of the paper states that, roughly speaking, each linear natural operator lifting $p$-vectors to tensor fields of type $(q,0)$ on $T^A$ is a sum of operators obtained by permuting the indices of the tensor products of linear natural operators lifting $p$-vectors to tensor fields of type $(p,0)$ on $T^A$ and canonical tensor fields of type $(q-p,0)$ on $T^A$.},

author = {Dębecki, Jacek},

journal = {Czechoslovak Mathematical Journal},

keywords = {natural operator; Weil bundle},

language = {eng},

number = {2},

pages = {511-525},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Linear natural operators lifting $p$-vectors to tensors of type $(q,0)$ on Weil bundles},

url = {http://eudml.org/doc/280099},

volume = {66},

year = {2016},

}

TY - JOUR

AU - Dębecki, Jacek

TI - Linear natural operators lifting $p$-vectors to tensors of type $(q,0)$ on Weil bundles

JO - Czechoslovak Mathematical Journal

PY - 2016

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 66

IS - 2

SP - 511

EP - 525

AB - We give a classification of all linear natural operators transforming $p$-vectors (i.e., skew-symmetric tensor fields of type $(p,0)$) on $n$-dimensional manifolds $M$ to tensor fields of type $(q,0)$ on $T^AM$, where $T^A$ is a Weil bundle, under the condition that $p\ge 1$, $n\ge p$ and $n\ge q$. The main result of the paper states that, roughly speaking, each linear natural operator lifting $p$-vectors to tensor fields of type $(q,0)$ on $T^A$ is a sum of operators obtained by permuting the indices of the tensor products of linear natural operators lifting $p$-vectors to tensor fields of type $(p,0)$ on $T^A$ and canonical tensor fields of type $(q-p,0)$ on $T^A$.

LA - eng

KW - natural operator; Weil bundle

UR - http://eudml.org/doc/280099

ER -

## References

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