Structure of a Class of Integrable Lie Algebras

In , for any complex n×n matrix A, we have a Lie algebra g(A). Ifthe Chevalley generators e_i, f_i=(i = 1,…,n) of g(A) are locally nilpotent, theng(A) is integrable. The central object of our study is this class of integrableLie algebras.Definition 1 A matrix A is said to be equivalent to a matrix B if there ex-ists a non-degenerate diagonal matrix D such thatDB=A(by reordering the indices)