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Von Neumann代数中的套子代数 总被引:2,自引:1,他引:2
本文主要讨论因子Von Neumann代数中套子代数上的线性满等距和自伴导子.证明了因子Von Neumann代数中套子代数上的每个线性满等距是同构乘酉算子或者是反同构乘酉算子;给出了其上自伴导子是内导子的条件并得到有限因子 Von Neumann代数中套子代数上的每个自伴导子都是内导子. 相似文献
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通过对复数域上单李代数的Loop代数进行一维导子扩张,得到一类无限维完备李代数;利用其根空间分解及无外导子的性质,证明了这类无限维完备李代数的2-局部齐次导子都是导子. 相似文献
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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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《数学的实践与认识》2020,(14)
构造了δ-Hom-Jordan李色代数,然后给出了δ-Hom-Jordan李色代数的α~k-导子的概念,进而得到了保积δ-Hom-Jordan李色代数的导子扩张. 相似文献
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《数学的实践与认识》2019,(23)
对filiform李代数R_n的triple导子进行了研究.利用triple导子的定义,通过计算线性变换在一组特殊的基上的作用结果,得到了filiform李代数R_n的triple导子的矩阵形式,并发现其triple导子代数是一个维数为2n-1的可解李代数. 相似文献
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本文研究了交换环上一个李超代数的导子.利用构造几类特殊的导子,获得了此李超代数的任意导子是几类特殊导子的和.推广了交换环上李代数的导子. 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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In this paper the authors investigate the structure of the restricted Lie algebra cohomology of p-nilpotent Lie algebras with trivial p-power operation. Our study is facilitated by a spectral sequence whose E 2-term is the tensor product of the symmetric algebra on the dual of the Lie algebra with the ordinary Lie algebra cohomology and converges to the restricted cohomology ring. In many cases this spectral sequence collapses, and thus, the restricted Lie algebra cohomology is Cohen–Macaulay. A stronger result involves the collapsing of the spectral sequence and the cohomology ring identifying as a ring with the E 2-term. We present criteria for the collapsing of this spectral sequence and provide some examples where the ring isomorphism fails. Furthermore, we show that there are instances when the spectral sequence does not collapse and yields cohomology rings which are not Cohen-Macaulay. 相似文献
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I.S. Rakhimov I.M. Rikhsiboev A.Kh. Khudoyberdiyev I.A. Karimjanov 《Linear algebra and its applications》2012,437(9):2209-2227
In this paper we describe the isomorphism classes of finite-dimensional complex Leibniz algebras whose quotient algebra with respect to the ideal generated by squares is isomorphic to the direct sum of three-dimensional simple Lie algebra sl2 and a three-dimensional solvable ideal. We choose a basis of the isomorphism classes’ representatives and give explicit multiplication tables. 相似文献
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A nonassociative algebra is defined to be zeropotent if the square of any element is zero. In this paper, we give a complete classification of three-dimensional zeropotent algebras over the real number field up to isomorphism. By restricting the result to the subclass of Lie algebras, we can obtain a classification of three-dimensional real Lie algebras, which is in accordance with the Bianchi classification. Moreover, three-dimensional zeropotent algebras over a real closed field are classified in the same manner as those over the real number field. 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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Fangyan Lu 《Journal of Functional Analysis》2006,240(1):84-104
A Lie isomorphism ? between algebras is called trivial if ?=ψ+τ, where ψ is an (algebraic) isomorphism or a negative of an (algebraic) anti-isomorphism, and τ is a linear map with image in the center vanishing on each commutator. In this paper, we investigate the conditions for the triviality of Lie isomorphisms from reflexive algebras with completely distributive and commutative lattices (CDCSL). In particular, we prove that a Lie isomorphism between irreducible CDCSL algebras is trivial if and only if it preserves I-idempotent operators (the sum of an idempotent and a scalar multiple of the identity) in both directions. We also prove the triviality of each Lie isomorphism from a CDCSL algebra onto a CSL algebra which has a comparable invariant projection with rank and corank not one. Some examples of Lie isomorphisms are presented to show the sharpness of the conditions. 相似文献
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《代数通讯》2013,41(4):1259-1277
ABSTRACT We study the varieties of Lie algebra laws and their subvarieties of nilpotent Lie algebra laws. We classify all degenerations of (almost all) five-step and six-step nilpotent seven-dimensional complex Lie algebras. One of the main tools is the use of trivial and adjoint cohomology of these algebras. In addition, we give some new results on the varieties of complex Lie algebra laws in low dimension. 相似文献
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In this article, we associate to affine algebraic or local analytic varieties their tangent algebra. This is the Lie algebra
of all vector fields on the ambient space which are tangent to the variety. Properties of the relation between varieties and
tangent algebras are studied. Being the tangent algebra of some variety is shown to be equivalent to a purely Lie algebra
theoretic property of subalgebras of the Lie algebra of all vector fields on the ambient space. This allows to prove that
the isomorphism type of the variety is determinde by its tangent algebra. 相似文献