构造相应于有限维非退化可解李代数的顶点代数

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{heiti $hat{g}$}的表示理论,构造出一类水平为l的限制$hat{g}$ -模$V_{hat{g}}(l,0)$.然后应用顶点算子的局部理论在hom$(V_{hat{g}}(l,0),V_{hat{g}}(l,0)((x)))$中 找到一类顶点代数$L_{V_{hat{g}}(l,0)}$.建立了$L_{V_{hat{g}}(l,0)}$到 $V_{hat{g}}(l,0)$的映射,最后证明了这类映射是顶点代数同构.

Vertex Algebra Associated to Nondegenerate Solvable Lie Algebras

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.