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- 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。
- 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。
- 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。
- 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;
- 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。
- In this paper, the conclusion is that the intersection of lie subring of a Lie group is a Lie subring is obtained, moreover,it gives the Lie algebra of the Lie subring. 文章通过李子群的性质得出了李群的两个李子群的交依然是李子群的结论,进而得出这一李子群的李代数形式。
- This is equivalent to an ordinary (non-projective) representation of the double cover of SO(p,q, R ), which is a real Lie group called the spinor group Spin(p,q). 是旋转群(李群SO(n;R) )的投影表象中的元素，或更广义地说，是SO(p;q;R)群的投影表象中的元素，其中p + q = n for spinors in a space of nontrivial signature.
- I have a house opposite lying dilapidated four grey buildings in crowded, as the giant towers between it really insignificant in the dwarf like limbs stunting. 我家对面有一栋低矮破旧的四层灰色楼房，在拥挤的、巨人般的塔楼之间，它的确渺小得像个四肢发育不全的侏儒。
- In this paper,by giving a left invariant and symplectic structure, we have discussed the left invariant vector field and Maurer-Cartan form on Lie group,and have drawn some conclusions on them. 文章通过对李群上赋予一个左不变的辛结构,对李群上的左不变向量场及左不变1一形式进行研究,得出相关结论。
- First, it is shown from a new viewpoint that the universal enveloping algebra generates a Lie subgroup of a known classical infinite dimensional Lie group, therefore the enlargability is ensured. 首先,本文从一个新的视角证明泛包络代数作为无穷维李代数生成一个标准无穷维李群的子李群,从而保证了泛包络代数的可扩张性;
- He tried to varnish over the truth with a lie. 他试图用谎言来掩盖真相。
- 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。
- I asked the man opposite if he would open the door. 我问对面的人他愿意不愿意开门。
- He came in and took a seat opposite to me. 他走进来，坐在我对面的座位上。
- 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。
- She played opposite Charles Chaplin in that film. 她在那部影片中兴查理。卓别林演对手戏。
- Put the wardrobe in the corner opposite the door. 把衣柜放在对着门的那个角落里。
- 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。
