  We study the Lie bialgebra structures that can be built on the
one-dimensional central extension of the Poincar\'e and (A)dS algebras in (1+1)
dimensions. These central extensions admit more than one interpretation, but
the simplest one is that they describe the symmetries of (the noncommutative
deformation of) an Abelian gauge theory, $U(1)$ or $SO(2)$ on the (1+1)
dimensional Minkowski or (A)dS spacetime. We show that this highlights the
possibility that the algebra of functions on the gauge bundle becomes
noncommutative. This is a new way in which the Coleman-Mandula theorem could be
circumvented by noncommutative structures, and it is related to a mixing of
spacetime and gauge symmetry generators when they act on tensor-product states.
We obtain all Lie bialgebra structures on centrally-extended Poincar\'e and
(A)dS which are coisotropic w.r.t. the Lorentz algebra, and therefore all of
them admit the construction of a noncommutative principal gauge bundle on a
quantum homogeneous Minkowski spacetime. It is shown that several different
types of hybrid noncommutativity between the spacetime and gauge coordinates
are allowed by introducing quantum extended Poincar\'e symmetries. In one of
these cases, an alternative interpretation of the central extension leads to a
new description of the well-known canonical noncommutative spacetime as the
quantum homogeneous space of a quantum Poincar\'e algebra of symmetries.
