Hodge type decomposition

Wojciech Kozłowski

Annales Polonici Mathematici, Tome 92 (2007), p. 99-104 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2007-01-01

Zbl 1111.53050

EUDML-ID : urn:eudml:doc:280301