A finite-dimensional Lie algebra arising from a Nichols algebra of diagonal type (rank 2)

Let B-q be a finite-dimensional Nichols algebra of diagonal type corresponding to a matrix q is an element of k (theta x theta). Let L-q be the Lusztig algebra associated to B-q [AAR]. We present L-q as an extension (as braided Hopf algebras) of B-q by 3q where 3(q) is isomorphic to the universal enveloping algebra of a Lie algebra n(q). We compute the Lie algebra nq when theta = 2.