Abstract
We consider the possible covariant external algebra structures for Cartan's 1-forms ( Omega ) on GLq(N) and SLq(N). Our starting point is that the Omega realize an adjoint representation of quantum group and all monomials of the Omega possess the unique ordering. For the external algebras obtained define the differential mapping d possessing the usual nilpotence condition, and the generally deformed version of the Leibnitz rules. The status of the known examples of GLq(N)-differential calculi in the proposed classification scheme and the problems of SLq(N)-reduction are discussed.
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