Automorphisms and derivations of Uq(sl4+)

AbstractWe compute the automorphism group of the q-enveloping algebra Uq(sl4+) of the nilpotent Lie algebra of strictly upper triangular matrices of size 4. The result obtained gives a positive answer to a conjecture of Andruskiewitsch and Dumas. We also compute the derivations of this algebra and then show that the Hochschild cohomology group of degree 1 of this algebra is a free (left) module of rank 3 (which is the rank of the Lie algebra sl4) over the center of Uq(sl4+)