  We introduce the framework of Hopf algebra field theory (HAFT) which
generalizes the notion of group field theory to the quantum group (Hopf
algebra) case. We focus in particular on the 3d case and show how the HAFT we
considered is topological. The highlight of the construction is the notion of
plane-wave which leads, in the specific example of SUq (2) with q real, to a
discretization of the Euclidian BF action with a negative cosmological
constant. This work can be viewed as the generalization of the seminal work by
Baratin and Oriti: we have a (non-commutative) formulation of simplicial 3d
gravity in the presence of a non-zero cosmological constant.
