Multi-parameter Quantum Groups related to link-diagrams

We apply the Faddeev-Reshetikhin-Taktajan method for the construction of Quantum Groups to the Yang-Baxter matrices which are related to the invariants of oriented links in Σ×[0,1], where Σ is a non-trivial 2-dimensional surface. We obtain multi-parameter ribbon Hopf algebras that differ in many respects from their one-parameter counterparts. Among the main differences we mention the existence of a non-central quantum determinant and the fact that the number of independent generators is higher than in the one-parameter case.