Blas Torrecillas

Let H be a quasi-Hopf algebra. To a set I and a given family of characters of H indexed by I, we associate a braided Hopf algebra within the category of Yetter-Drinfeld modules over H. 

This kind of free braided Hopf algebra can be, moreover, factorized through some Serre relations, leading thus to the construction of the Drinfeld-Jimbo quantum groups in the quasi-Hopf setting. 

Our construction is an extremely general one (even in the Hopf case, the Drinfeld Jimbo quantum groups U_q(g) are obtained as a particular case of our construction) and allows us not only to introduce the quasi-Hopf analog of the U_q(g)'s, but also to define new classes of quasi-quantum groups (joint work with Daniel Bulacu).