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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、辛流形及群胚等為基本研究對象。
- Using the Lie group theory and method, we presented a necessary condition for the existence of generalized symmetry of ordinary differential equations. 摘要利用李群理論和方法給出了自治常微分方程存在某類特殊廣義對稱的必要條件。
- Furthermore,this course is benefitial to study differential topology, Riemannian Geometry, Lie group and Nonlinear Analysis etc. 為進一步學習微分幾何、微分拓撲、幾何分析、黎曼幾何、李群、低維拓撲和非線性分析等相關課程奠定良好的基礎，並為閱讀當代數學文獻創造條件。
- Lie Groups, Lie Algebras, and Their Representation by V.S. 最重要的李群、李代數參考書;
- Lie groups and algebraic groups, by A. L. Onishchik, E. B. 李群的參考書;
- Any symmetric space corresponds to a Lie group and an involution of it.The associated twisted conjugate action is related to the involution. 每個對稱空間對應著一個李群及這個李群的一個對合自同構，相應的扭共軛作用與這個對合自同構有關。
- 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. 文章通過李子群的性質得出了李群的兩個李子群的交依然是李子群的結論,進而得出這一李子群的李代數形式。
- 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). 是旋轉群(李群SO(n;R) )的投影表象中的元素，或更廣義地說，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. 我家對面有一棟低矮破舊的四層灰色樓房，在擁擠的、巨人般的塔樓之間，它的確渺小得像個四肢發育不全的侏儒。
- 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. 文章通過對李群上賦予一個左不變的辛結構,對李群上的左不變向量場及左不變1一形式進行研究,得出相關結論。
- 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,本文從一個新的視角證明泛包絡代數作為無窮維李代數生成一個標準無窮維李群的子李群,從而保證了泛包絡代數的可擴張性;
- He tried to varnish over the truth with a lie. 他試圖用謊言來掩蓋真相。
- Chevalley, Claude. Theory of Lie groups, I. Princeton, Princeton University Press, 1946. 《李群理論（一）》.;普林斯頓:普林斯頓大學出版社;1946年
- The text however develops basic Riemannian Geometry, Complex Manifolds, as well as a detailed theory of Semisimple Lie Groups and Symmetric Spaces. 然而課程還將簡單介紹了基本的黎曼幾何和複流形的知識，並會詳細討論半單李群和對稱空間的理論。
- I asked the man opposite if he would open the door. 我問對面的人他願意不願意開門。
- He came in and took a seat opposite to me. 他走進來，坐在我對面的座位上。
- We first prove the theorem on equivariant embedding of symmetric spaces in Lie groups. 首先，我們證明對稱空間到李群的等變嵌入定理。
- She played opposite Charles Chaplin in that film. 她在那部影片中興查理。卓別林演對手戲。
- Put the wardrobe in the corner opposite the door. 把衣櫃放在對著門的那個角落裡。
- But twisted conjugate actions of Lie groups have closed relation with nonabelian cohomology of cyclic groups with coefficients in Lie groups. 而李群的扭共軛作用與循環群以李群為係數的非交換上同調有非常密切的關係。
