  For a group G, the notion of a ribbon G-category was introduced by the second
author in a previous work with a view towards constructing 3-dimensional
homotopy quantum field theories (HQFT's) with target K(G,1). We discuss here
how to derive ribbon G-categories from a simple complex Lie algebra g where G
is the center of g. The construction is based on a study of representations of
the quantum group $U_q(g)$ at a root of unity. Under certain assumptions on the
root of unity, the resulting G-categories give rise to numerical invariants of
pairs (a closed oriented 3-manifold M, an element of $H^1(M;G)$) and to
3-dimensional HQFT's.
