有限维非退化可解李代数顶点算子代数模的结构

Study on structure of modules of vertex operator algebra of finite-dimensional nondegenerate solvable Lie algebra

李代数是一类重要的非结合代数,它与众多数学分支都有紧密的联系,并且是物理学的重要研究工具.顶点算子代数是一种在共形场论及相关的物理领域中很重要的一种代数结构.顶点算子代数在纯数学领域如魔鬼月光中很有用.设g是有限维非退化可解非幂零李代数.V^g(l,0)为相应于g的顶点算子代数,得到了以下结果:W是相应于g的顶点代数(V^g(l,0),YV,1)模当且仅当W是的g的仿射李代数^g的水平为l的限制模;g的顶点算子代数的不可分解模存在子模的合成列.

Lie algebra was a kind of nonassociative algebra,which was closely related to many branches of mathematics and it was an important research tool of physics. Vertex operator algebra was an important algebraic structure in conformal field theory and related fields of physics. Vertex operator algebra was useful in purely mathematical fields such as Montreal smoonshine. Letgbe a finite-dimensional nondegenerate solvable nonnilpotent Liealgebra. In this paper,the following results were presented:any module for vertex algebracoincided with the restrictedmodule of level;there existed the composition series of submoduleson any indecomposable vertex operator algebra module.