We characterize symmetry transformations of Lagrangian extremals generating “on shell” conservation laws. We relate symmetry transformations of extremals to Jacobi fields and study symmetries of higher variations by proving that a pair given by a symmetry of the lth variation of a Lagrangian and by a Jacobi field of the sth variation of the same Lagrangian (with s < l) is associated with an “off shell” conserved current. The conserved current associated with two symmetry transformations is constructed, and as a case of study, its expression for invariant sets of Yang–Mills connections on Minkowski space-times is obtained.

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