Linear liftings of skew-symmetric tensor fields to Weil bundles

Dębecki, Jacek. "Linear liftings of skew-symmetric tensor fields to Weil bundles." Czechoslovak Mathematical Journal 55.3 (2005): 809-816. <http://eudml.org/doc/30990>.

@article{Dębecki2005,
abstract = {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.},
author = {Dębecki, Jacek},
journal = {Czechoslovak Mathematical Journal},
keywords = {natural operator; product preserving bundle functor; Weil algebra; natural operator; product preserving bundle functor; Weil algebra},
language = {eng},
number = {3},
pages = {809-816},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Linear liftings of skew-symmetric tensor fields to Weil bundles},
url = {http://eudml.org/doc/30990},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Dębecki, Jacek
TI - Linear liftings of skew-symmetric tensor fields to Weil bundles
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 3
SP - 809
EP - 816
AB - 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.
LA - eng
KW - natural operator; product preserving bundle functor; Weil algebra; natural operator; product preserving bundle functor; Weil algebra
UR - http://eudml.org/doc/30990
ER -