低维幂零李代数的导子代数-基础数学专业论文.docxVIP

万方数据 万方数据 Master Dissertation of Suzhou University of Science and Technology Derivation algebras of low dimensional nilpotent Lie algebras Master Candidate: Pan Linhui Supervisor: Professor Ren Bin Major: Fundamental Mathematics Suzhou University of Science and Technology School of Mathematics and Physics June, 2014 苏州科技 苏州科技学院硕士学位论文 摘 要 摘 要 研究李代数的导子代数，是其结构理论研究的重要方面。复数域上半单李代 数的导子代数已经研究清楚，相比之下，幂零李代数的导子代数还远未研究清楚, 原因是幂零李代数的结构极端复杂。找出导子的各种等价条件是刻画出李代数的 导子代数的有效途径。二步幂零李代数是一种重要的幂零李代数，其结构相对简 单。本文通过矩阵的巧妙计算，得到了三维中心的二步幂零李代数导子的一个充 要条件。利用该等价条件，计算出了二维中心的八维二步幂零李代数的不同构类 的导子。 关键词：基；极小生成元系；幂零李代数；导子代数 I Mas Master Dissertation of Suzhou University of Science and Technology Abstract Abstract It is an important aspect for studying on the structure theory to research the derivation algebras of Lie algebras. The derivation algebras of semisimple Lie algebras over complex field C have been studied clearly, by contrast, the derivation algebras of nilpotent Lie algebras have not been studied clearly, because the structure of nilpotent Lie algebras is extremely complex. It is an effective way for characterizing the derivation algebra of a Lie algebra to find out some equivalent conditions of the derivation. Two step nilpotent Lie algebras is a kind of important nilpotent Lie algebras, and it has relatively simple structure. In this paper, by ingenious calculation of the matrix, a sufficient and necessary condition for the derivation of two step nilpotent Lie algebras with three dimensional center is obtained . Using the equivalent condition, the derivations of two step nilpotent Lie algebra of eight dimension with two dimension center of nonisomorphic classes are calculated. Keyword: Basis; Minimal system of generator; Nilpotent Lie algebra; Derivation algebra II 苏州科 苏州科技学院硕士学位论文 目 录 目 录 HYPERLINK \l _bookmark0 摘 要 .................................................................................................................................................I HYPERLINK \l _bookmark1 Abstract