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

✍ Scribed by Anastasios Mallios; Patrice P. Ntumba


Book ID
107627042
Publisher
Springer Milan
Year
2009
Tongue
Italian
Weight
285 KB
Volume
58
Category
Article
ISSN
0009-725X

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A class of geometric structures defined by i + l-forms that generalize the notion of a symplectlc form is introduced. Examples of these structures occur in multi-dimensional variational calculus. An extension of the Darboux-Moser-Weinstein theorem is proved for these structures and a charactenzataon

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Let k be a C1-ÿeld of characteristic zero. Let A be an a ne algebra of dimension d ¿ 2 over k. In this set up, Suslin proved that the free module A d is cancellative (in other words, stably free A-modules of rank d are free). In this note we show that, in fact, all ÿnitely generated projective A-mod