  Let $\Gamma$ be an $N^2$-dimensional bicovariant first order differential
calculus on a Hopf algebra $SL_q(N)$. There are three possibilities to
construct a differential Z-graded Hopf algebra $\Gamma^\wedge$ which contains
$\Gamma$ as its first order part. Let $q$ be a transcendental complex number.
For $N>2$ these three Z-graded Hopf algebras coincide. For Woronowicz' external
algebra we calculate the dimensions of the spaces of left-invariant and
bi-invariant $k$-forms. In this case each bi-invariant form is closed. In case
of $4D_\pm$ calculi on $SL_q(2)$ the universal calculus is strictly larger than
the other two calculi. In particular, the bi-invariant 1-form is not closed.
