共查询到20条相似文献,搜索用时 62 毫秒
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《数学的实践与认识》2013,(17)
在李代数的研究中,经常使用算子李代数的结构去刻划其它李代数的代数结构,由算子构成的李代数在李代数理论中占有重要的位置.构造了算子李代数g(G,M)[σ]的子代数,然后讨论了这些子代数的代数结构. 相似文献
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研究了一类带单参数q的无限维Block型李代数,这类李代数是Virasoro-like李代数的推广. Virasoro-like李代数是一类非常重要的无限维李代数.本文研究了这类李代数子代数,同构和同态. 相似文献
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研究了带双参数的a,b的无限维W(a,b)型李代数,这类李代数是Virasoro李代数的推广.本文研究了这类李代数的两类子代数,一类子代数同构无中心的Virasoro李代数,另一类子代数是交换李子代数,并且是理想.研究了这类李代数同构和同态,证明了g不是单李代数. 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
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V. V. Gorbatsevich 《Russian Mathematics (Iz VUZ)》2018,62(4):29-41
In this paper we introduce and study dual Lie algebras, i.e., Lie algebras over the algebra of dual numbers. We establish some fundamental properties of such Lie algebras and compare them with the corresponding properties of real and complex Lie algebras. We discuss the question of classification of dual Lie algebras of small dimension and consider the connection of dual Lie algebras with approximate Lie algebras. 相似文献
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Complemented Lie algebras are introduced in this paper (a notion similar to that studied by O. Loos and E. Neher in Jordan pairs). We prove that a Lie algebra is complemented if and only if it is a direct sum of simple nondegenerate Artinian Lie algebras. Moreover, we classify simple nondegenerate Artinian Lie algebras over a field of characteristic 0 or greater than 7, and describe the Lie inner ideal structure of simple Lie algebras arising from simple associative algebras with nonzero socle. 相似文献
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Ling Chen 《数学学报(英文版)》2011,27(1):45-72
We construct a class of new Lie algebras by generalizing the one-variable Lie algebras generated by the quadratic conformal
algebras (or corresponding Hamiltonian operators) associated with Poisson algebras and a quasi-derivation found by Xu. These
algebras can be viewed as certain twists of Xu’s generalized Hamiltonian Lie algebras. The simplicity of these algebras is
completely determined. Moreover, we construct a family of multiplicity-free representations of these Lie algebras and prove
their irreducibility. 相似文献
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A metric Lie algebra is a Lie algebra equipped with an invariant non-degenerate symmetric bilinear form. It is called indecomposable if it is not the direct sum of two metric Lie algebras. We are interested in describing the isomorphism classes of indecomposable metric Lie algebras. In the present paper we restrict ourselves to a certain class of solvable metric Lie algebras which includes all indecomposable metric Lie algebras with maximal isotropic centre. We will see that each metric Lie algebra belonging to this class is a twofold extension associated with an orthogonal representation of an abelian Lie algebra. We will describe equivalence classes of such extensions by a certain cohomology set. In particular we obtain a classification scheme for indecomposable metric Lie algebras with maximal isotropic centre and the classification of metric Lie algebras of index 2. 相似文献
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Kurt Meyberg 《manuscripta mathematica》1970,3(2):115-132
In this paper we study certain Lie algebras which are constructed from the (-1)-eigenspaees of an involution of a Jordan algebra. The construction is a generalisation of the Koecher-Tits-construction. We give necessary conditions in terms of the Jordan algebras for the Lie algebras being simple. If the (-1)-spaces are Peirce-1/2-components then we obtain a close relation between the Lie algebras under consideration and the structure algebras of Jordan algebras. We finally give a list of those types of simple Lie algebras which can be formed by this construction; among them are Lie algebras of type E6 and E7.Of fundamental importance for our considerations is a close connection between the constructed Lie algebras and the standard imbeddings of Lie triple systems. 相似文献
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COMPLETE LIE ALGEBRAS WITH l-STEP NILPOTENT RADICALS 总被引:2,自引:2,他引:0
The authors first give a necessary and sufficient condition for some solvable Lie algebras with l-step nilpotent radicals to be complete, and then construct a new class of infinite dimensional complete Lie algebras by using the modules of simple Lie algebras. The quotient algebras of this new constructed Lie algebras are non-solvable complete Lie algebras with l-step nilpotent radicals. 相似文献
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姜玉秋 《数学的实践与认识》2009,39(3)
算子群作为群的推广,算子群在群论里有许多应用.类似地,作为算子群和李代数的推广,算子李代数将会有许多应用.给出了算子李代数的一些性质,得到了算子李代数半单性的充分必要条件.同时得到算子李代数半单性与非退化killing型的关系. 相似文献
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The notion of generating index of Lie algebras is introduced. We characterize some Lie algebras with full generating index
and classify the Lie algebras with generating index 2 and 3. As a corollary, we give a characterization of 2-step nilpotent
Lie algebras. 相似文献
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In this paper we introduce the notion of Jordan socle for nondegenerate Lie algebras, which extends the definition of socle given in [A. Fernández López et al., 3-Graded Lie algebras with Jordan finiteness conditions, Comm. Algebra, in press] for 3-graded Lie algebras. Any nondegenerate Lie algebra with essential Jordan socle is an essential subdirect product of strongly prime ones having nonzero Jordan socle. These last algebras are described, up to exceptional cases, in terms of simple Lie algebras of finite rank operators and their algebras of derivations. When working with Lie algebras which are infinite dimensional over an algebraically closed field of characteristic 0, the exceptions disappear and the algebras of derivations are computed. 相似文献