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The symplectic Gram-Schmidt theorem and fundamental geometries for $𝒜$ -modules

Patrice P. Ntumba — 2012

Czechoslovak Mathematical Journal

Like the classical Gram-Schmidt theorem for symplectic vector spaces, the sheaf-theoretic version (in which the coefficient algebra sheaf $𝒜$ is appropriately chosen) shows that symplectic $𝒜$ -morphisms on free $𝒜$ -modules of finite rank, defined on a topological space $X$ , induce canonical bases (Theorem 1.1), called symplectic bases. Moreover (Theorem 2.1), if $(ℰ, φ)$ is an $𝒜$ -module (with respect to a $ℂ$ -algebra sheaf $𝒜$ without zero divisors) equipped with an orthosymmetric $𝒜$ -morphism, we show, like in the classical...

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The symplectic Gram-Schmidt theorem and fundamental geometries for 𝒜 -modules

The symplectic Gram-Schmidt theorem and fundamental geometries for $𝒜$ -modules