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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(lèi)特殊廣義對稱(chēng)的必要條件。
- Furthermore,this course is benefitial to study differential topology, Riemannian Geometry, Lie group and Nonlinear Analysis etc. 為進(jìn)一步學(xué)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(xiàn)性分析等相關(guān)課程奠定良好的基礎，并為閱讀當代數學(xué)文獻創(chuàng )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(shū);
- Lie groups and algebraic groups, by A. L. Onishchik, E. B. 李群的參考書(shū);
- 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(gè)對稱(chēng)空間對應著(zhù)一個(gè)李群及這個(gè)李群的一個(gè)對合自同構，相應的扭共軛作用與這個(gè)對合自同構有關(guān)。
- 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(guò)李子群的性質(zhì)得出了李群的兩個(gè)李子群的交依然是李子群的結論,進(jìn)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(shuō)，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.
- 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(guò)對李群上賦予一個(gè)左不變的辛結構,對李群上的左不變向量場(chǎng)及左不變1一形式進(jìn)行研究,得出相關(guān)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(gè)新的視角證明泛包絡(luò )代數作為無(wú)窮維李代數生成一個(gè)標準無(wú)窮維李群的子李群,從而保證了泛包絡(luò )代數的可擴張性;
- He tried to varnish over the truth with a lie. 他試圖用謊言來(lái)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(xué)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(jiǎn)單介紹了基本的黎曼幾何和復流形的知識，并會(huì )詳細討論半單李群和對稱(chēng)空間的理論。
- We first prove the theorem on equivariant embedding of symmetric spaces in Lie groups. 首先，我們證明對稱(chēng)空間到李群的等變嵌入定理。
- But twisted conjugate actions of Lie groups have closed relation with nonabelian cohomology of cyclic groups with coefficients in Lie groups. 而李群的扭共軛作用與循環(huán)群以李群為系數的非交換上同調有非常密切的關(guān)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. 而把同樣的性質(zhì)應用到恒同自同構，我們會(huì )得到李群中有限階共軛類(lèi)的閉性定理。
- Education should not be restricted to any one specific age group. 教育不應限制在任何特定的年齡組上。
- In particular, we prove that there are only finitely many equivalence classes for twisted conjugate actions for semisimple Lie groups. 特別地，我們證明了連通半單李群的扭共軛作用只有有限多個(gè)等價(jià)類(lèi)。
- The text for this class is Differential Geometry, Lie Groups and Symmetric Spaces by Sigurdur Helgason (American Mathematical Society, 2001). 然而課程還將簡(jiǎn)單介紹了基本的黎曼幾何和復流形的知識，并會(huì )詳細討論半單李群和對稱(chēng)空間的理論。
- He broke away from that lawless group years ago. 他在幾年前脫離了那個(gè)非法團體。
