  We define two subalgebras which can be seen as the quantization of the
coordinate rings of the unipotent radical of the standard positive
(respectively negative) Borel subgroup of $SL_{n+1}$. We give a presentation
for these algebras and show they are isomorphic. Moreover, we show that these
algebras are the conivariants of a natural $O_q(T)$-coaction on $O_q(B^\pm)$.
Finally, using a dual pairing, we show that these algebras are isomorphic to
the quantum nilpotent Lie subalgebra of $U_q(\mathfrak{sl}_{n+1})$.
