基于算子李代数的子代数结构研究  

Study on the Sub-algebra Structure Based on Operator Lie Algebra

作　　者：陆长安[1] 

机构地区：[1]陕西工商职业学院,陕西西安710119

出　　处：《山东农业大学学报（自然科学版）》2015年第4期618-620,共3页Journal of Shandong Agricultural University：Natural Science Edition

摘　　要：李代数是重要的非结合代数,对于代数结构的刻划,使用较多的是算子李代数结构,这也是李代数理论的重要组成部分。本文针对顶点算子代数的研究,提出一种基于算子李代数的子代数结构,由L1[σ]、L2[σ]两类子代数构造算子李代数g(G,M)[σ],论述了向量空间的生成,并根据两类子代数的定理与结构证明,为顶点算子代数的研究工作提供理论基础。The Lie algebra is important non-associative algebra, its algebraic structure to be used more is the operator Lie algebra, it is an important part of the theory of lie algebra. According to the research of vertex operator algebra, this paper put forward a kind of sub-algebra structure based on operator Lie algebra structure, L1[σ]、L2[σ] two kinds of sub-algebra structure made of operator Lie algebra g(G,M)[σ] to discuss the generation of vector space and take the theorem and structure of two classes of sub-algebra as the proof to provide the theoretical basis for the research work of vertex operator algebra.

关 键 词：李代数 代数结构 算子李代数 子代数 

分 类 号：O171[理学—数学]