Hodge type decomposition

Wojciech Kozłowski. "Hodge type decomposition." Annales Polonici Mathematici 90.2 (2007): 99-104. <http://eudml.org/doc/280301>.

@article{WojciechKozłowski2007,
abstract = {In the space $Λ^p$ of polynomial p-forms in ℝⁿ we introduce some special inner product. Let $H^p$ be the space of polynomial p-forms which are both closed and co-closed. We prove in a purely algebraic way that $Λ^p$ splits as the direct sum $d*(Λ^\{p+1\}) ⊕ δ*(Λ^\{p-1\}) ⊕ H^p$, where d* (resp. δ*) denotes the adjoint operator to d (resp. δ) with respect to that inner product.},
author = {Wojciech Kozłowski},
journal = {Annales Polonici Mathematici},
keywords = {Hodge theorem; polynomial -form},
language = {eng},
number = {2},
pages = {99-104},
title = {Hodge type decomposition},
url = {http://eudml.org/doc/280301},
volume = {90},
year = {2007},
}

TY - JOUR
AU - Wojciech Kozłowski
TI - Hodge type decomposition
JO - Annales Polonici Mathematici
PY - 2007
VL - 90
IS - 2
SP - 99
EP - 104
AB - In the space $Λ^p$ of polynomial p-forms in ℝⁿ we introduce some special inner product. Let $H^p$ be the space of polynomial p-forms which are both closed and co-closed. We prove in a purely algebraic way that $Λ^p$ splits as the direct sum $d*(Λ^{p+1}) ⊕ δ*(Λ^{p-1}) ⊕ H^p$, where d* (resp. δ*) denotes the adjoint operator to d (resp. δ) with respect to that inner product.
LA - eng
KW - Hodge theorem; polynomial -form
UR - http://eudml.org/doc/280301
ER -