N ) DIFFERENTIAL CALCULUS FROM THE DIFFERENTIAL CALCULUS ON GL q ( N ) ∗

We show that the Faddeev-Pyatov SL q (N) differential algebra [1] is a subalgebra of the GL q (N) differential algebra constructed by Schupp, Watts and Zumino [2]. In the paper [1], the bicovariant differential algebra on SL q (N) (see below (10), (11)) with generators {T ij , L ij , ˜ Ω ij } i, j = 1,. .. N has been constructed. The elements T ij are generators of the algebra F un(SL q (N)), while L ij generate a matrix of the right-invariant Lie derivatives on SL q (N) and the elements˜Ω ij define the basis of the right-invariant differential 1-forms on SL q (N). It has been shown [1] that this algebra is consistent with imposing the conditions: det q (T) = Det q (L) = 1 , T r q (˜ Ω) = 0 , (1) where we use Det q (L) = det q (LT) 1 det q (T) , T r q (˜ Ω) = N i=1 q −N −1+2i˜Ω ii .