Classification of Graded, Finite-Dimensional Lie Algebras of Vector Fields

摘要

We study finite-dimensional Lie algebras of vector fields on R(sub n), thatcontain the elements partial derivative with respect to X(sub i) and X(sub i) partial derivative with respect to X(sub i) for i = 1...n. To any Lie algebra L of this class, we associate an N-valued n x n-matrix A and a set of special elements S included in (left brace) 1,...,n (right brace). We prove that the pair (A,S) necessarily satisfies 2 properties. Conversely, to any pair (A,S) satisfying those 2 properties we associate a Lie algebra L(A,S), such that L(A,S) is maximal in the class of all L with matrix A and special elements S.