Cocycles on a finite dimensional quotient of uq (sl(2))

We prove that certain algebra quotients of Hopf algebras are twisted Hopf algebras. On the other handu_q (sl(2)) is a crossed product of a central subalgebra with a quotient Ubar], when q is a root of 1. Using the cocycle involved in this crossed product we construct non-trivial complex cocycles τ and we find the isomorphism classes of the corresponding twisted Hopf algebras _τ Ubar]. These provide complex projective representations of Ubar] which are not ordinary representations.