Let n be the nilpotent Lie algebra consisting of all strictly upper triangular (n + 1) x (rt + 1) matrices over a commutative ring R. In this paper, we discuss the automorphism group of n. We prove that any automorphism phi of n can be uniquely expressed as phi = omega . eta . xi . mu . sigma, where omega, eta, xi, mu and sigma are graph, diagonal, external, central and inner automorphisms, respectively, of n when n greater than or equal to 3 and R is a local ring that contains 2 as a unit or an integral domain of characteristic other than two. In the case n = 2 we also prove that any automorphism of n can be expressed as a product of graph, diagonal, extremal and inner automorphisms for an arbitrary local ring R. (C) 2001 Elsevier Science Inc. All rights reserved. [References: 8]
展开▼
