共查询到19条相似文献,搜索用时 46 毫秒
1.
本文旨在讨论有限维李代数及某些广义李代数的结构常数及相应的立方阵 ,从而获得一种新的从元素运算的角度的方法来刻划它们 ,即将对有限维李代数及某些广义李代数的讨论可转化为对 n× n× n立方阵的讨论。 相似文献
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Let n ≥ 4. The complex Lie algebra, which is attached to the unit form q(x1, x2,..., xn)■ and defined by generators and generalized Serre relations, is proved to be a finite-dimensional simple Lie algebra of type Dn, and realized by the Ringel-Hall Lie algebra of a Nakayama algebra. As its application of the realization, we give the roots and a Chevalley basis of the simple Lie algebra. 相似文献
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本文讨论了无限维完备李代数的一些性质,由Virasoro代数,Kac-Moody代数构造了几类无限维完备李代数.同时给出了Kac-Moody代数及其广义抛物子代数的导子代数的刻划.证明了完备李代数的Loop扩张仍为完备李代数. 相似文献
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小特征的有限维Cartan型李代数的滤过 总被引:1,自引:0,他引:1
张永正 《数学年刊A辑(中文版)》1995,(6)
用L表示Cartan型李代数W(n,m),S(n,m)或H(n,m〕.本文证明了当基域F的特征数p=2与3时L的自然滤过是不变的.从而得到了当p=2与3时,L的每个自同构都是由与之相应的除幂代数的自同构所诱导的. 相似文献
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本文研究民具有无限维中心的Toroidal李代数.通过利用其明确的生成元,确定了其上所有的非交换Poisson代数结构,从而推广了有限维中心的情形. 相似文献
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本文讨论了无限继完备李代数的一些性质,由Virasoro代数,Kac-Moody代数构造了几类无限维完备李代数.同时给出了Kac-Moody代数及其广义抛物子代数的导子代数的刻划.证明了完备李代数的Loop扩张仍为完备李代数。 相似文献
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首先证明了有限维Z-阶化李代数上的一个线性算子是Hom-结构的充分必要条件,即它的每个齐次分支也是Hom-结构.然后计算了特征零代数闭域上一类有限维Z-阶化Filiform李代数Qn的齐次Hom-结构,从而决定了Qn的所有Hom-结构. 相似文献
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Toroidal李代数上的Poisson代数结构 总被引:2,自引:0,他引:2
非交换的Poisson代数同时具有结合代数和李代数两种代数结构,而结合代数和李代数之间满足所谓的Leibniz法则.文中确定了Toroidal李代数上所有的Poisson代数结构,推广了仿射Kac-Moody代数上相应的结论. 相似文献
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The paper investigates simple multilinear algebras, known as comtrans algebras, that are determined by Lie algebras and by pairs of matrices. The two classes of algebras obtained in this way separate, except for the vector triple product algebra. 相似文献
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Consuelo Martínez 《Mediterranean Journal of Mathematics》2006,3(2):273-282
The aim of this work is to provide a survey of some of the main structural results about graded algebras, in both, Lie and
Jordan cases and relate them with some results about infinite dimensional superalgebras.
Partially supported by MTM 2004 08115-C04-01 and FICYT IB05-186. 相似文献
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Ivan Marin 《代数通讯》2013,41(7):2572-2584
We consider the natural Lie algebra structure on the (associative) group algebra of a finite group G, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a decomposition in simple factors of these Lie algebras, in terms of the ordinary representations of G. 相似文献
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In this paper we shall prove the main part ((3) implies (1))of the following theorem. The proof of the theorem will be completedin a forthcoming paper [6]. 相似文献
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A Class of Infinite Dimensional Simple Lie Algebras 总被引:1,自引:0,他引:1
Let A be an abelian group, F be a field of characteristic 0,and , ß be linearly independent additive maps fromA to F, and let ker()\{0}. Then there is a Lie algebra L = L(A,, ß, ) = xA Fex under the product [ex, ey]]=(xy)ex+y+(ß) (x, y) ex+y. If, further, ß() = 1, and ß(A) = Z, thereis a subalgebra L+:=L(A+, , ß, ) = xA+ Fex, whereA+ = {xA|ß(x)0}. The necessary and sufficient conditionsare given for L' = [L, L] and L+ to be simple, and all semi-simpleelements in L' and L+ are determined. It is shown that L' andL+ cannot be isomorphic to any other known Lie algebras andL' is not isomorphic to any L+, and all isomorphisms betweentwo L' and all isomorphisms between two L+ are explicitly described. 相似文献
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K. N. Raghavan 《代数通讯》2013,41(10):3783-3785
It is observed that there are no non-trivial finite dimensional inductive algebras for a connected group. 相似文献
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V. V. Trofimov 《Journal of Mathematical Sciences》2000,102(6):4668-4671
In this paper, the definition of the maximal exponent for Lie algebras corresponding to compact simple Lie groups is given.
For this purpose, the imbeddings of finite groups by regular elements in compact Lie groups are used.
Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 74, Algebra-15,
2000. 相似文献
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本文给出了树型代数的拟遗传序数的精确上界以及单生成元的树型代数的拟遗传序数的精确下界及其算法 ,并由此得到一个新的组合公式 . 相似文献