A class of bicovariant differential calculi on hopf algebras

We introduce a large class of bicovariant differential calculi on any quantum group A, associated to Ad-invariant elements. For example, the deformed trace element on SL_q (2) recovers Woronowicz's 4D_± calculus. More generally, we obtain a class of differential calculi on each quantum group A(R), based on the theory of the corresponding braided groups B(R). Here R is any regular solution of the QYBE.Supported by St John's College, Cambridge and KBN grant 2 0218 91 01.