Similarities are shown between the algebras of differential forms and of Clifford algebra-valued multi-vector functions in an open region of Euclidean space. The Poincar´e Lemma and the Dual Poincar´e Lemma are restated and proved in a refined version. In the case of real-analytic differential forms an alternative proof of the Poincar´e Lemma is given using the Euler operator. A position is taken in the debate on the redundancy of either of the two algebras.
@article{1547,
title = {Differential Forms and/or Multi-vector Functions},
journal = {CUBO, A Mathematical Journal},
volume = {7},
year = {2005},
language = {en},
url = {http://dml.mathdoc.fr/item/1547}
}
Brackx, F.; Delanghe, R.; Sommen, F. Differential Forms and/or Multi-vector Functions. CUBO, A Mathematical Journal, Tome 7 (2005) 31 p. http://gdmltest.u-ga.fr/item/1547/