I will describe how one can use the representation theory of finite-dimensional factorizable ribbon Hopf algebras H as a laboratory for studying aspects of logarithmic conformal field theories. In particular, certain H-bimodules F and K play the role of the space of bulk states and of the so-called bulk handle Hopf algebra of the CFT, while bimodule morphisms involving these two objects correspond to correlation functions of bulk fields.

The object F has a natural structure of a commutative symmetric Frobenius algebra and is naturally a K-module. With the help of these structures, an explicit construction is given of candidates for the morphisms which play the role bulk field correlators on closed surfaces of any genus, and it is shown that they are invariant under the relevant action of the mapping class group.