A Central Extension Theorem-for Hopf Algebras

The construction used in Schur's central extension theorem is generalized by proving that given a cocommutative Hopf algebra H, there is a cocornmutative central extension B of H such that any projective representation of H lifts to an ordinary representation of B. The extension B is the crossed product of H with the finite dual of the group algebra kZ₁, where Z₁denotes the group of normal cocycles on H with values in the ground field k.