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Keywords:
fibered manifold; jet space; Lagrangian formalism; variational sequence; second variational derivative; cohomology; symmetry; conservation law
fibered manifold; jet space; Lagrangian formalism; variational sequence; second variational derivative; cohomology; symmetry; conservation law
Summary:
We consider cohomology defined by a system of local Lagrangian and investigate under which conditions the variational Lie derivative of associated local currents is a system of conserved currents. The answer to such a question involves Jacobi equations for the local system. Furthermore, we recall that it was shown by Krupka et al. that the invariance of a closed Helmholtz form of a dynamical form is equivalent with local variationality of the Lie derivative of the dynamical form; we remark that the corresponding local system of Euler–Lagrange forms is variationally equivalent to a global one.
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