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The variational Lie derivative of classes of forms in the Krupka'svariational sequence is defined as a variational Cartan formula at any degree,in particular for degrees lesser than the dimension of the basis manifold. Asan example of application we determine the condition for aNoether--Bessel-Hagen current, associated with a generalized symmetry, to bevariationally equivalent to a Noether current for an invariant Lagrangian. Weshow that, if it exists, this Noether current is exact on-shell and generates acanonical conserved quantity.

Variational derivatives in locally Lagrangian field theories and Noether--Bessel-Hagen currents