  In the Hamiltonian formulation of general relativity, Einstein's equation is
replaced by a set of four constraints. Classically, the constraints can be
identified with the generators of the hypersurface-deformation Lie algebroid
(HDA) that belongs to the groupoid of finite evolutions in space-time. Taken
over to deformed general relativity, this connection allows one to study
possible Drinfeld twists of space-time diffeomorphisms with Hopf-algebra
techniques. After a review of noncommutative differential structures, two cases
--- twisted diffeomorphisms with standard action and deformed (or $\star$-)
diffeomorphisms with deformed action --- are considered in this paper. The HDA
of twisted diffeomorphisms agrees with the classical one, while the HDA
obtained from deformed diffeomorphisms is modified due to the explicit presence
of $\star$-products in the brackets. The results allow one to distinguish
between twisted and deformed symmetries, and they indicate that the latter
should be regarded as the relevant symmetry transformations for noncommutative
manifolds. The algebroid brackets maintain the same general structure
regardless of space-time noncommutativity, but they still show important
consequences of non-locality.
