Graded Lie algebra associated to a SODE (Q2714217)
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scientific article; zbMATH DE number 1604048
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Graded Lie algebra associated to a SODE |
scientific article; zbMATH DE number 1604048 |
Statements
12 June 2001
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inverse problem
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calculus of variations
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Euler-Lagrange equation
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variational multiplier
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spray
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connection
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derivations
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0.9160623
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0.9147886
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0.9112394
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0.9111409
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Graded Lie algebra associated to a SODE (English)
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The paper introduces a graded Lie algebra associated to a second order differential equation. The key is to use the Frolicher-Nijenhuis theory of derivation associated with vector valued form, combined with the concept of sprays introduced by Klein for solving the inverse problem of the variational calculus. In this framework, one derives some identities satisfied by variational sprays, and then one defines a Lie algebra associated to a spray. Two theorems are stated which allow one to see whether a given spray is variational or not. The author claims in his abstract that his approach is a powerful tool.
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