  We construct lattice gauge field theory based on a quantum group on a lattice
of dimension 1. Innovations include a coalgebra structure on the connections,
and an investigation of connections that are not distinguishable by
observables. We prove that when the quantum group is a deformation of a
connected algebraic group (over the complex numbers), then the algebra of
observables forms a deformation quantization of the ring of characters of the
fundamental group of the lattice with respect to the corresponding algebraic
group. Finally, we investigate lattice gauge field theory based on quantum
SL(2,C), and conclude that the algebra of observables is the Kauffman bracket
skein module of a cylinder over a surface associated to the lattice.
