  In this paper we study quantum group deformations of the infinite dimensional
symmetry algebra of asymptotically AdS spacetimes in three dimensions. Building
on previous results in the finite dimensional subalgebras we classify all
possible Lie bialgebra structures and for selected examples, we explicitly
construct the related Hopf algebras. Using cohomological arguments we show that
this construction can always be performed by a so-called twist deformation. The
resulting structures can be compared to the well-known $\kappa$-Poincar\'e Hopf
algebras constructed on the finite dimensional Poincar\'e or (anti) de Sitter
algebra. The dual $\kappa$ Minkowski spacetime is supposed to describe a
specific non-commutative geometry. Importantly, we find that some incarnations
of the $\kappa$-Poincar\'e can not be extended consistently to the infinite
dimensional algebras. Furthermore, certain deformations can have potential
physical applications if subalgebras are considered. Since the conserved
charges associated with asymptotic symmetries in 3-dimensional form a centrally
extended algebra we also discuss briefly deformations of such algebras. The
presence of the full symmetry algebra might have observable consequences that
could be used to rule out these deformations. }
