CLASSIFICATION OF BICOVARIANT DIFFERENTIAL CALCULI

We show that the bicovariant first-order differential calculi on a fac torisable quantum group with the Peter-Weyl decomposition property are in 1-1 correspondence with irreducible representations V of the quant um group enveloping algebra. The corresponding calculus is constructed and has dimension dimV(2). The differential calculi on a finite group algebra CG are also classified and shown to be in correspondence with pairs consisting of an irreducible representation V and a continuous parameter in CPdimV-1. They have dimension dimV. For a classical Lie g roup we obtain an infinite family of non-standard calculi. General con structions for bicovariant calculi and their quantum tangent spaces ar e also obtained. (C) 1998 Elsevier Science B.V.