构造相应于有限维非退化可解李代数的顶点代数

Vertex Algebra Associated to Nondegenerate Solvable Lie Algebras

设g是带有非退化不变对称双线性型的有限维可解李代数,该文首先应用g的仿射李代数g的表示理论,构造出一类水平为l的限制g-模Vg(l,0)．然后应用顶点算子的局部理论在hom(Vg(l,0),Vg(l,0)((x)))中找到一类顶点代数LVg(l,0)．建立了LVg(l,0)到Vg(l,0)的映射,最后证明了这类映射是顶点代数同构．

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 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.