A BICOVARIANT DIFFERENTIAL ALGEBRA OF A QUANTUM GROUP

A bicovariant differential algebra of four basic objects (coordinate functions, differential 1-forms, Lie derivatives and inner derivations) within a differential calculus on a quantum group is shown to be produced by a direct application of the cross-product construclion to the Wolonowicz differential complex, whose Hopf algebra properties account for the bicovariance of the algebra. A correspondence with classical differential calculus, including Cartan identity, and some other useful relations are considered. An explicit construction of a bicovariant differencial algebra on GLq(N) K given and its (co)module pruperties are discussed.