精品文档---下载后可任意编辑交换环上严格上三角矩阵的双导子和套代数上非线性三元 Lie 导子的开题报告题目：交换环上严格上三角矩阵的双导子和套代数上非线性三元 Lie导子摘要：本文讨论了交换环上严格上三角矩阵的双导子和套代数上非线性三元 Lie 导子的性质。首先介绍了严格上三角矩阵和 Lie 代数的基本定义和性质，然后探讨了严格上三角矩阵的双导子的定义和性质。接着，介绍了套代数及其基础知识，然后引入非线性三元 Lie 导子的定义和性质，并在此基础上推导套代数上非线性三元 Lie 导子的一些性质。最后，通过实例验证了所得结论的正确性。关键词：严格上三角矩阵，Lie 代数，双导子，套代数，非线性三元Lie 导子Abstract:We study the properties of double derivations of strictly upper triangular matrices on commutative rings and non-linear ternary Lie derivatives on enveloping algebras. First we introduce the basic definitions and properties of strictly upper triangular matrices and Lie algebras, then discuss the definition and properties of double derivations of strictly upper triangular matrices. Next, we introduce the basic knowledge of enveloping algebras, and then introduce the definition and properties of non-linear ternary Lie derivatives, and derive some properties of non-linear ternary Lie derivatives on enveloping algebras. Finally, we verify the correctness of the obtained conclusions through examples.Keywords: Strictly Upper Triangular Matrix, Lie Algebra, Double Derivations, Enveloping Algebras, Non-Linear Ternary Lie Derivatives.
