Let , be finite-dimensional Lie algebras over a field of characteristic zero. Regard and , the dual Lie coalgebra of , as Lie bialgebras with zero cobracket and zero bracket, respectively. Suppose that a matched pair of Lie bialgebras is given, which has structure maps . Then it induces a matched pair of Hopf algebras, where is the universal envelope of and is the Hopf dual of . We show that the group of cleft Hopf algebra extensions associated with is naturally isomorphic to the group of Lie bialgebra extensions associated with . An exact sequence involving either of these groups is obtained, which is a variation of the exact sequence due to G.I. Kac. If , there follows a bijection between the set of all cleft Hopf algebra extensions of by and the set of all Lie bialgebra extensions of by .
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共查询到18条相似文献，搜索用时 31 毫秒
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本文刻划了一类幂零根基为二步幂零李代数的新的非可解对称自对偶李代数．当其Ｌｅｖｉ因子同构于ｓｌ（２，Ｃ）时，用半单李代数的表示理论具体构造了它们．最后，给出了■２中对称自对偶李代数是ＣＳ李代数的一个判别准则。 相似文献
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带有非退化不变对称双线性型的有限维可解李代数 总被引：3，自引：0，他引：3
本文讨论复数域上带有非退化不变对称双线性型的,可裂的有限维可解李代数的性质及结构.给出了不可分解的非退化可解李代数的定义.证明了本文所讨论的李代数可以分解成不可分解的非退化可解理想的正交直和.对于不可分解的非退化可解李代数,给出了它关于极大环面子代数的根空间分解;讨论了根空间的结构及运算关系;证明了它的 Cartan 子代数的交换性,并给出了 Cartan子代数的结构. 相似文献
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一类带有非退化不变对称双线性函数的幂零李代数 总被引：1，自引：1，他引：0
本文证明了一类带有非退化不变对称双线性函数、幂零指数为Ｎ的李代数 满足：定理１．（ｉ）ｃ（ｇ）＝ｇ~Ｎ; （ｉｉ）ｄｉｍｃ（ｇ）＝ｌ．ｌ是ｇ的生成元个数．定理３给出了这类李代数结构的充分且必要条件． 相似文献
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三次可解型非退化李代数及其导子李代数的结构 总被引：1，自引：1，他引：0
本文给出了非退化可解李代数的两个类型:三次可解型非退化李代数和扩充的 Heisenberg李代数,并确定三次可解型非退化李代数及其导子李代数的结构． 相似文献
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本文讨论了完备李代数的同构问题,并对幂零根基为一些Ｈｅｉｓｅｎｂｅｒｇ代数及交换李代数之直和的可解和一般完备李代数的结构进行了讨论． 相似文献
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Akira Masuoka 《Transactions of the American Mathematical Society》2000,352(8):3837-3879
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Xusheng LIU 《数学年刊B辑(英文版)》2006,27(3):287-302
By making use of the classification of real simple Lie algebra, we get the maximum of the squared length of restricted roots case by case, and thus get the upper bounds of sectional curvature for irreducible Riemannian symmetric spaces of compact type. As an application, this paper verifies Sampson's conjecture in most cases for irreducible Riemannian symmetric spaces of noncompact type. 相似文献
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Xusheng LIU 《数学年刊B辑(英文版)》2008,29(3):317-332
In this paper, the partial positivity （resp., negativity） of the curvature of all irreducible Riemannian symmetric spaces is determined. From the classifications of abstract root systems and maximal subsystems, the author gives the calculations for symmetric spaces both in classical types and in exceptional types. 相似文献
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Boris Širola 《代数通讯》2013,41(9):3267-3279
Suppose G 1 ? G are complex linear simple Lie groups. Let 1 ? be the corresponding pair of Lie algebras. For the Killing-orthogonal of 1 in we have a vector space direct sum = 1⊕ , which generalizes the classical Cartan decomposition on the Lie algebras level. In this article we study the corresponding problem of a ‘generalized global Cartan decomposition’ on the Lie groups level for the pair of groups ( G , G 1) = (SL (4,?),Sp (2,?)); here = (4,?), 1 = (2,?), and = {X ? | X ? = X}, where X? X ? is the symplectic involution. We prove that G = G 1exp ∪ i G 1exp . The key point of the proof is to study in detail the set exp ; and for that purpose we introduce the J-twisted Pfaffian of size 2n defined on the set of all 2n × 2n matrices X satisfying X ? = X, which is here a natural counterpart of the standard Pfaffian. 相似文献
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A-扩张Lie Rinehart代数 总被引：1，自引：0，他引：1
The purpose of this paper is to give a brief introduction to the category of Lie Rinehart algebras and introduces the concept of smooth manifolds associated with a unitary, commutative,associative algebra A.It especially shows that the A-extended algebra as well as the action algebra can be realized as the space of A-left invariant vector fields on a Lie group,analogous to the well known relationship of Lie algebras and Lie groups. 相似文献
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