共查询到20条相似文献,搜索用时 687 毫秒
1.
本文给出了无限秩仿射李代数的某种类型的Cartan子代数的定义,并证明了这种Cartan子代数在无限秩仿射李代数的某种类型的自同构下的共轭性. 相似文献
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证明了有限维Jordan李代数的Engel定理,并应用它得到了Jordan李代数的Cartan子代数的若干性质. 相似文献
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董泉发 《数学年刊A辑(中文版)》2015,36(3):325-334
构造了Cartan型李代数W(n;m)的一类Borel子代数φ(n;m),其中n是一个正整数,且m=(m_1,…,m_n)是一个n-元正整数数组.确定了φ(n;m)的导子代数.特别地,φ(n;1)是一个Cartan型完备阶化李代数,它不同于任何典型完备李代数. 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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<正> 复半单李代数的 Weyl 群在复半单李代数理论中占有极重要的地位.由于复半单李代数的 Cartan 子代数是内共轭的,因此复半单李代数的 Weyl 群的讨论比较简单.熟知,实半单李代数的 Cartan 子代数不一定是内共轭的,而不内共轭的 Cartan 子代数有不同的 Weyl 群.本文的目的就是企图得出实半单李代数的所有不内共轭的 Cartan 子代数的 Weyl 群.由于实半单李代数的 Cartan 子代数的内共轭分类,已被许多作者讨论得非 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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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
11.
The paper shows how to associate a motivic zeta function with a
large class of infinite dimensional Lie algebras. These include
loop algebras, affine Kac-Moody algebras, the Virasoro algebra
and Lie algebras of Cartan type. The concept of a motivic zeta
functions provides a good language to talk about the uniformity
in p of local
p-adic zeta functions of finite dimensional
Lie algebras. The theory of motivic integration is employed to
prove the rationality of motivic zeta functions associated to
certain classes of infinite dimensional Lie algebras. 相似文献
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Zha Jianguo 《东北数学》1998,(4)
1.InfiniteRankAfineLieAlgebrasg(X)andg(X)WerecalthedefinitionofinfiniterankafineLiealgebrasandtheirfundamentalstructure.Agene... 相似文献
13.
Xiaoping Xu 《Journal of Pure and Applied Algebra》2008,212(6):1253-1309
We construct irreducible modules of centrally-extended classical Lie algebras over left ideals of the algebra of differential operators on the circle, through certain irreducible modules of centrally-extended classical Lie algebras of infinite matrices with finite number of nonzero entries. The structures of vertex algebras associated with the vacuum representations of these algebras are determined. Moreover, we prove that under certain conditions, the highest-weight irreducible modules of centrally-extended classical Lie algebras of infinite matrices with finite number of nonzero entries naturally give rise to the irreducible modules of the simple quotients of these vertex algebras. From vertex algebra and its representation point of view, our results with positive integral central charge are high-order differential operator analogues of the well-known WZW models in conformal field theory associated with affine Kac-Moody algebras. Indeed, when the left ideals are the algebra of differential operators, our Lie algebras do contain affine Kac-Moody algebras as subalgebras and our results restricted on them are exactly the representation contents in WZW models. Similar results with negative central charge are also obtained. 相似文献
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We find generators and relations for those subalgebras of Kac-Moody Lie algebras that are the fixed point algebras of certain involutions. Specifically the involution must involve the Cartan involution which interchanges the positive and negative generators. We go on to apply these results to the G.I.M. algebras, which were introduced as natural generalizations of Kac-Moody algebras by P. Slodowy. We show such algebras are isomorphic to subalgebras of Kac-Moody algebras. From this we are able to derive someinteresting interrelations between certain Kac-Moody algebras. 相似文献
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N. A. Koreshkov 《Siberian Mathematical Journal》2013,54(3):472-478
We prove some analogs of the Lie and Engel theorems for n-tuple Lie algebras. Furthermore, we establish existence of Cartan subalgebras in the n-tuple Lie algebras. 相似文献
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We extend conjugacy results from Lie algebras to their Leibniz algebra generalizations. The proofs in the Lie case depend on anti-commutativity. Thus it is necessary to find other paths in the Leibniz case. Some of these results involve Cartan subalgebras. Our results can be used to extend other results on Cartan subalgebras. We show an example here and others will be shown in future work. 相似文献
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ZHU Linsheng Department of Mathematics Changshu Institute of Technology Changshu China 《中国科学A辑(英文版)》2006,49(4):477-493
A Lie algebra endowed with a nondegenerate, symmetric, invariant bilinear form is called a quadratic Lie algebra. In this paper, the author investigates the structure of solvable quadratic Lie algebras, in particular, the solvable quadratic Lie algebras whose Cartan subalgebras consist of semi-simple elements, the author presents a procedure to construct a class of quadratic Lie algebras from the point of view of cohomology and shows that all solvable quadratic Lie algebras can be obtained in this way. 相似文献
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Salvatore Siciliano 《代数通讯》2013,41(12):4513-4522
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V. V. Shuvalov 《Functional Analysis and Its Applications》2002,36(4):298-305
In this paper, the commutative (with respect to the Poisson bracket) subalgebras in the Poisson algebras of the semisimple Lie algebras are considered on condition that these subalgebras are limits of Mishchenko--Fomenko subalgebras. We study the case of the degeneration within a fixed Cartan subalgebra. The structure of the limit subalgebras is described (i.e., it is proved that these subalgebras are free, and their generators are found). The classification of the limit subalgebras of the above type is also established. 相似文献
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Sh. M. Kasymov 《Algebra and Logic》1995,34(4):223-231
One of the most profound results in the theory of Lie algebras states that any two Cartan subalgebras of a finite-dimensional Lie algebra over an algebraically closed field of characteristic 0 are conjugate relative to the group of special automorphisms generated by the exponents of nilpotent inner derivations. Using some new ideas, we prove an analog of this statement for n-ary n-Lie algebras. Other interesting properties of Cartan algebras, which are known to be shared by Lie algebras, are carried over to n-Lie algebras.Translated fromAlgebra i Logika, Vol. 34, No. 4, pp. 405–419, July-August, 1995. 相似文献