Vertex Algebra Associated to Nondegenerate Solvable Lie Algebras
构造相应于有限维非退化可解李代数的顶点代数

The main purpose of this article is to construct the vertex algebra of associated to finite-nondegenerate solvable Lie algebra. Avoid the notion of module of vertex algebra and tire some the Jacobi identity. Apply the equivalent condition with the Jacobi identity:the weak commutativity and the D-derivatve-bracket formula. On the theorems of the representation of finite-nondegenerate solvable Lie algebra g and the level l restricted module of the affine algebra $\hat{g}$ of g. Construct and prove a kind the vertex algebras , which equipped the structure of different with that the vertex algebra of associated to Heisenberg algebra and non-twist Kac-moody algebra.