  We investigate the automorphism group of the quantised enveloping algebra U
of the positive nilpotent part of certain simple complex Lie algebras g in the
case where the deformation parameter q \in \mathbb{C}^* is not a root of unity.
Studying its action on the set of minimal primitive ideals of U we compute this
group in the cases where g=sl_3 and g=so_5 confirming a Conjecture of
Andruskiewitsch and Dumas regarding the automorphism group of U. In the case
where g=sl_3, we retrieve the description of the automorphism group of the
quantum Heisenberg algebra that was obtained independently by Alev and Dumas,
and Caldero. In the case where g=so_5, the automorphism group of U was computed
in [16] by using previous results of Andruskiewitsch and Dumas. In this paper,
we give a new (simpler) proof of the Conjecture of Andruskiewitsch and Dumas in
the case where g=so_5 based both on the original proof and on graded arguments
developed in [17] and [18].
