Automorphisms and derivations of U-q (sl(4)(+))

Abstract

We compute the automorphism group of the q-enveloping algebra U-q(sl(+)(4)) of the nilpotent Lie algebra of strictly upper 4 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 I of this algebra is a free (left) module of rank 3 (which is the rank of the Lie algebra Sl(4)) over the center of U-q(sl(4)(+))