Fundamentals for symplectic \(\mathcal{A}\)-modules. Affine Darboux theorem

DOI10.1007/s12215-009-0015-1zbMath1211.18011arXiv0712.1271OpenAlexW1569401276MaRDI QIDQ2379905

Anastasios Mallios, Patrice P. Ntumba

Publication date: 23 March 2010

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.1271

zbMATH Keywords

abstract differential geometryvector sheaf\(\mathcal{A}\)-moduleaffine Darboux theoremordered \(\mathbb{R}\)-algebraized spacesymplectic group sheafsympletic \(\mathcal{A}\)-structure

Mathematics Subject Classification ID

Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20) Abstract manifolds and fiber bundles (category-theoretic aspects) (18F15)

Related Items (8)

The symplectic Gram-Schmidt theorem and fundamental geometries for A-modules ⋮ Cartan-Dieudonné theorem for \({\mathcal {A}}\)-modules ⋮ On the commutativity of the Clifford and ``extension of scalars functors ⋮ Complexification in \(A\)-modules ⋮ \(A\)-transvections and Witt's theorem in symplectic \(A\)-modules ⋮ Clifford \({\mathcal{A}}\)-algebras of quadratic \({\mathcal{A}}\)-modules ⋮ Witt's theorem in abstract geometric algebra ⋮ Grassmann sheaves and the classification of vector sheaves

Cites Work

• On a sheaf-theoretic version of the Witt's decomposition theorem. A Lagrangian perspective
• Multilinear algebra. 2nd ed
• Lectures on symplectic geometry
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