COVARIANTIZATION OF QUANTIZED CALCULI OVER QUANTUM GROUPS.

We introduce a method for construction of a covariant differential calculus over a Hopf algebra A from a quantized calculus da = [D, a], a ∈ A, where D is a candidate for a Dirac operator for A. We recover the method of construction of a bicovariant differential calculus given by T. Brzeziński and S.Majid created from a central element of the dual Hopf algebra A°. We apply this method to the Dirac operator for the quantum SL(2) given by S.Majid. We find that the differential calculus obtained by our method is the standard bicovariant 4D-calculus. We also apply this method to the Dirac operator for the quantum SL(2) given by P.N.Bibikov and P.P.Kulish and show that the resulted differential calculus is 8-dimensional. [ABSTRACT FROM AUTHOR]