A Central Extension Theorem-for Hopf Algebras

摘要

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