A generalization of the exterior product of differential forms combining Hom-valued forms

Gross, Christian. "A generalization of the exterior product of differential forms combining Hom-valued forms." Commentationes Mathematicae Universitatis Carolinae 38.3 (1997): 587-602. <http://eudml.org/doc/248094>.

@article{Gross1997,
abstract = {This article deals with vector valued differential forms on $C^\infty $-manifolds. As a generalization of the exterior product, we introduce an operator that combines $\operatorname\{Hom\}(\bigotimes ^s(W),Z)$-valued forms with $\operatorname\{Hom\}(\bigotimes ^s(V),W)$-valued forms. We discuss the main properties of this operator such as (multi)linearity, associativity and its behavior under pullbacks, push-outs, exterior differentiation of forms, etc. Finally we present applications for Lie groups and fiber bundles.},
author = {Gross, Christian},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {differential forms; exterior product; multilinear algebra; differential forms; exterior product; multilinear algebra},
language = {eng},
number = {3},
pages = {587-602},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A generalization of the exterior product of differential forms combining Hom-valued forms},
url = {http://eudml.org/doc/248094},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Gross, Christian
TI - A generalization of the exterior product of differential forms combining Hom-valued forms
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 3
SP - 587
EP - 602
AB - This article deals with vector valued differential forms on $C^\infty $-manifolds. As a generalization of the exterior product, we introduce an operator that combines $\operatorname{Hom}(\bigotimes ^s(W),Z)$-valued forms with $\operatorname{Hom}(\bigotimes ^s(V),W)$-valued forms. We discuss the main properties of this operator such as (multi)linearity, associativity and its behavior under pullbacks, push-outs, exterior differentiation of forms, etc. Finally we present applications for Lie groups and fiber bundles.
LA - eng
KW - differential forms; exterior product; multilinear algebra; differential forms; exterior product; multilinear algebra
UR - http://eudml.org/doc/248094
ER -