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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 ( , φ ) is an 𝒜 -module (with respect to a -algebra sheaf 𝒜 without zero divisors) equipped with an orthosymmetric 𝒜 -morphism, we show, like in the classical...

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