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- Lie Groups, Lie Algebras, and Their Representation by V.S. 最重要的李群、李代数参考书;
- Lie groups and algebraic groups, by A. L. Onishchik, E. B. 李群的参考书;
- Chevalley, Claude. Theory of Lie groups, I. Princeton, Princeton University Press, 1946. 《李群理论（一）》.;普林斯顿:普林斯顿大学出版社;1946年
- The text however develops basic Riemannian Geometry, Complex Manifolds, as well as a detailed theory of Semisimple Lie Groups and Symmetric Spaces. 然而课程还将简单介绍了基本的黎曼几何和复流形的知识，并会详细讨论半单李群和对称空间的理论。
- We first prove the theorem on equivariant embedding of symmetric spaces in Lie groups. 首先，我们证明对称空间到李群的等变嵌入定理。
- But twisted conjugate actions of Lie groups have closed relation with nonabelian cohomology of cyclic groups with coefficients in Lie groups. 而李群的扭共轭作用与循环群以李群为系数的非交换上同调有非常密切的关系。
- And if we apply the same property to the identity automorphism, we get the closedness theorem for conjugacy classes of finite order in Lie groups. 而把同样的性质应用到恒同自同构，我们会得到李群中有限阶共轭类的闭性定理。
- In particular, we prove that there are only finitely many equivalence classes for twisted conjugate actions for semisimple Lie groups. 特别地，我们证明了连通半单李群的扭共轭作用只有有限多个等价类。
- The text for this class is Differential Geometry, Lie Groups and Symmetric Spaces by Sigurdur Helgason (American Mathematical Society, 2001). 然而课程还将简单介绍了基本的黎曼几何和复流形的知识，并会详细讨论半单李群和对称空间的理论。
- In this paper,Lie group,Symplectic manifolds,Groupoids are treated as fundamental research subjects . 本文主要以李群、辛流形及群胚等为基本研究对象。
- Discrete subgroups of Lie groups are foundational objects in modern mathematics and occur naturally in different subjects. 李群的离散群在现代数学中是非常基础的概念，广泛地应用于不同的学科。
- Moreover, some results on nonabelian cohomology of finite cyclic groups with coefficients in Lie groups can be also generalized to the case of finite non-cyclic groups. 而有限循环群李群系数非交换上同调的一些结果，还可以推广到有限非循环群的情况。
- It goes on to describe the representation theory of compact Lie groups, including the application of integration to establish Weyl's formula in this context. 它接着描述小型谎话组的代表理论，包括综合的应用建立韦尔的这上下文公式。
- Then, by letting the automorphism in a theorem in Chapter 2 to be the identity, we get the closedness theorem for conjugacy classes of finite order in Lie groups. 随后，我们在第二章的某个定理中取自同构为恒同映射的特殊情况，证明了李群中有限阶共轭类的闭性定理，并给出了一个关于李群中某些共轭类是闭子流形的猜测。
- Using the Lie group theory and method, we presented a necessary condition for the existence of generalized symmetry of ordinary differential equations. 摘要利用李群理论和方法给出了自治常微分方程存在某类特殊广义对称的必要条件。
- He tried to varnish over the truth with a lie. 他试图用谎言来掩盖真相。
- Applying a property of orbit structures of twisted conjugate actions to involutions, we then get the aforementioned equivariant embedding of symmetric spaces in Lie groups. 利用本文中证明的李群扭共轭作用的轨道性质，将扭共轭作用中的自同构取为对合自同构，我们就得到了如上所述的对称空间在李群中的等变嵌入。
- Furthermore,this course is benefitial to study differential topology, Riemannian Geometry, Lie group and Nonlinear Analysis etc. 为进一步学习微分几何、微分拓扑、几何分析、黎曼几何、李群、低维拓扑和非线性分析等相关课程奠定良好的基础，并为阅读当代数学文献创造条件。
- Any symmetric space corresponds to a Lie group and an involution of it.The associated twisted conjugate action is related to the involution. 每个对称空间对应着一个李群及这个李群的一个对合自同构，相应的扭共轭作用与这个对合自同构有关。
- We also propose a conjecture on the closedness of certain conjugacy classes in Lie groups, whose generalization has been proved by the author in his later work. 这一猜测的推广在作者后来的工作中得到了证明。
