  In general relativity as well as gauge theories, non-trivial symmetries can
appear at boundaries. In the presence of radiation some of the symmetries are
not Hamiltonian vector fields, hence the definition of charges for the
symmetries becomes delicate. It can lead to the problem of field-dependent
2-cocycles in the charge algebra, as opposed to the central extensions allowed
in standard classical mechanics. We show that if the Wald-Zoupas prescription
is implemented, its covariance requirement guarantees that the algebra of
Noether currents is free of field-dependent 2-cocycles, and its stationarity
requirement further removes central extensions. Therefore the charge algebra
admits at most a time-independent field-dependent 2-cocycle, whose existence
depends on the boundary conditions. We report on new results for asymptotic
symmetries at future null infinity that can be derived with this approach.
