AUTOMORPHISMS OF CERTAIN NILPOTENT LIE ALGEBRAS OVER COMMUTATIVE RINGS

Let L be a finite-dimensional complex simple Lie algebra, Lℤ be the ℤ-span of a Chevalley basis of L and LR = R⊗ℤLℤ be a Chevalley algebra of type L over a commutative ring R. Let $\mathcal{N}(R)$ be the nilpotent subalgebra of LR spanned by the root vectors associated with positive roots. The aim of this paper is to determine the automorphism group of $\mathcal{N}(R)$.