Prolongation of Poisson \(2\)-form on Weil bundles. (Q2828837)
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scientific article; zbMATH DE number 6644061
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Prolongation of Poisson \(2\)-form on Weil bundles. |
scientific article; zbMATH DE number 6644061 |
Statements
26 October 2016
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Weil bundle
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Weil algebra
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Poisson manifold
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Lie derivative
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Poisson 2-form
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Prolongation of Poisson \(2\)-form on Weil bundles. (English)
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Let \(M\) be an \(n\)-dimensional smooth manifold and \(A\) be a Weil algebra. The associated Weil bundle is denoted as \(\pi_{M}:M^A\to M\). Geometrical objects on \(M\) can be lifted to geometrical object on \(M^A\). In the paper the authors study lifts of 2-forms \(\omega_M\) on \(M\) to \(A\)-valued 2-forms \(\omega^A_{M^A}\). If \((M,\omega_M)\) is a Poisson manifold then a necessary and sufficient condition for \((M^A,\omega^A_{M^A})\) to be an \(A\)-Poisson manifold are found.
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