Pairings of Sheaves of $\mathcal{A}$-Modules through Bilinear $\mathcal{A}$-Morphisms

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dc.creatorMallios, A.
dc.creatorNtumba, PP
dc.date2008-04-22
dc.date.accessioned2026-07-07T09:33:59Z
dc.date.available2026-07-07T09:33:59Z
dc.descriptionIt is proved that for any free $\mathcal{A}$-modules $\mathcal{F}$ and $\mathcal{E}$ of finite rank on some $\mathbb{C}$-algebraized space $(X, \mathcal{A})$ a \textit{degenerate} bilinear $\mathcal{A}$-morphism $Φ: \mathcal{F}\times \mathcal{E}\longrightarrow \mathcal{A}$ induces a \textit{non-degenerate} bilinear $\mathcal{A}$-morphism $\barΦ: \mathcal{F}/\mathcal{E}^\perp\times \mathcal{E}/\mathcal{F}^\perp\longrightarrow \mathcal{A}$, where $\mathcal{E}^\perp$ and $\mathcal{F}^\perp$ are the \textit{orthogonal} sub-$\mathcal{A}$-modules associated with $\mathcal{E}$ and $\mathcal{F}$, respectively. This result generalizes the finite case of the classical result, which states that given two vector spaces $W$ and $V$, paired into a field $k$, the induced vector spaces $W/V^\perp$ and $V/W^\perp$ have the same dimension. Some related results are discussed as well.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/0804.3481
dc.identifierhttp://arxiv.org/abs/0804.3481
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159329
dc.subjectSymplectic Geometry
dc.subjectGeneral Mathematics
dc.subject47A07
dc.titlePairings of Sheaves of $\mathcal{A}$-Modules through Bilinear $\mathcal{A}$-Morphisms
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