  Surface charges and their algebra in interacting Lagrangian gauge field
theories are investigated by using techniques from the variational calculus. In
the case of exact solutions and symmetries, the surface charges are interpreted
as a Pfaff system. Integrability is governed by Frobenius' theorem and the
charges associated with the derived symmetry algebra are shown to vanish. In
the asymptotic context, we provide a generalized covariant derivation of the
result that the representation of the asymptotic symmetry algebra through
charges may be centrally extended. Finally, we make contact with Hamiltonian
and with covariant phase space methods.
