Automorphisms Of The Nilpotent Subalgebra Generated By Positive Root Vectors Of Chevalley Algebra Of Type A_n, D_n, E₆ Over Local Rings

Let R be a local ring. Let N be the nilpotent subalgebra generated by positive root vectors of chevalley algebra of type An ( n 3),Dn (n 4),E6 over R. In this paper, we discuss the automorphism group of N. We prove that any automorphism of N can be expressed as = g . v . dx . g . . i, where g, v, dx, , and i are graph, exceptional, diagonal, extremal, central and inner automorphisms, respectively, of N, and that if Ann(2) = 0, the automorphism group Aut (N) = , where and 3 are the graph, diagonal, extremal, central and inner automorphism groups, respectively, of N, we also discuss the automorphism group of N generated by positive root vectors of chevalley algebra of type A1,A2.