共查询到20条相似文献,搜索用时 105 毫秒
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令R是有单位元1的2-挠自由交换环, L_n(R)是由R上所有n阶反对称矩阵构成的李代数.本文研究了L_n(R)(n≥3)上局部导子和2-局部导子的性质.利用L_n(R)作为李代数的完备性和矩阵计算技巧,证明了L_n(R)上的每个局部导子和2-局部导子都是导子.推广了L_n(R)上关于导子的主要结果. 相似文献
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每一个Jordan代数都对应了一个Tits-Kantor-Koecher李代数.在扩张仿射李代数的分类中[1],A1型李代数的分类依赖于欧氏空间上半格给出的Tits-Kantor-Koecher李代数.另外在相似的意义下,二维欧氏空间R2中只有两个半格.设S是R2上的任一半格,Τ(S)为半格S对应的Jordan代数,(g)(Τ(S))为相应的Tits.Kantor-Koecher李代数.利用Wakimoto自由场的方法给出李代数(g)(Τ(S))的一类顶点表示. 相似文献
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本文主要研究非In型因子VonNeumann代数的Nest子代数及两元生成格自反代数的可加导子的自动线性性和连续性问题.通过给出一个含无限维交换VonNeumann子代数的代数上可加导子定理,证明了非In型因子VonNeumann代数的Nest子代数上的可加导子是线性的,从而是自动连续的.这推广并简化证明了作者[1]中的主要结果.对于在非自伴算子代数研究中起重要的两元生成格自反代数,给出了所有可加导子是线性导子的充分必要条件. 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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本文给出了复数域C上的具有有限多个理想的有限维李代数L的结构:L=S+ Cr+ N,其中 S为 Levi因子,Cr+N为根基,N为幂零根基.当 N为交换时,文中还给出具有这种结构的李代数L具有有限多个理想的充要条件,并且将N为Heisenberg代数或亚交换李代数的惰形的讨论归结为N是交换的情形. 相似文献
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设R是一个含有单位元的2无扰的交换环,M_2(R)是定义在R上的全矩阵代数,证明了M_2(R)上的每一个非线性Lie导子都可以表示成一个内导子,一个可加诱导导子和一个映所有二次换位子为零的中心映射的和. 相似文献
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关于完满的Lie超代数 总被引:1,自引:0,他引:1
In this paper, some properties of perfect Lie superalgebras are investigated. We prove that the derivation superalgebra of a centerless perfect Lie superalgebra of arbitrary dimension over a field of arbitrary characteristic is complete and we obtain a necessary and sufficient condition for the holomorph of a centerless perfect Lie superalgebra to be complete. Finally, some properties of perfect restricted Lie superalgebras are given. 相似文献
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A. Beauville 《Commentarii Mathematici Helvetici》1998,73(4):566-583
A contact structure on a complex manifold M is a corank 1 subbundle F of TM such that the bilinear form on F with values in the quotient line bundle L = TM/F deduced from the Lie bracket of vector fields is everywhere non-degenerate. In this paper we consider the case where M
is a Fano manifold; this implies that L is ample.?If is a simple Lie algebra, the unique closed orbit in (for the adjoint action) is a Fano contact manifold; it is conjectured that every Fano contact manifold is obtained in this
way. A positive answer would imply an analogous result for compact quaternion-Kahler manifolds with positive scalar curvature,
a longstanding question in Riemannian geometry.?In this paper we solve the conjecture under the additional assumptions that
the group of contact automorphisms of M is reductive, and that the image of the rational map M
P(H
0(M, L)*) sociated to L has maximum dimension. The proof relies on the properties of the nilpotent orbits in a semi-simple
Lie algebra, in particular on the work of R. Brylinski and B. Kostant.
Received: July 28, 1997 相似文献
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We establish a correspondence (or duality) between the characters and the crystal bases of finite-dimensional representations
of quantum groups associated to Langlands dual semi-simple Lie algebras. This duality may also be stated purely in terms of
semi-simple Lie algebras. To explain this duality, we introduce an “interpolating quantum group” depending on two parameters
which interpolates between a quantum group and its Langlands dual. We construct examples of its representations, depending
on two parameters, which interpolate between representations of two Langlands dual quantum groups. 相似文献
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Rajeev Walia 《Advances in Mathematics》2009,222(5):1649-1686
In this paper we discuss the “Factorization phenomenon” which occurs when a representation of a Lie algebra is restricted to a subalgebra, and the result factors into a tensor product of smaller representations of the subalgebra. We analyze this phenomenon for symmetrizable Kac-Moody algebras (including finite-dimensional, semi-simple Lie algebras). We present a few factorization results for a general embedding of a symmetrizable Kac-Moody algebra into another and provide an algebraic explanation for such a phenomenon using Spin construction. We also give some application of these results for semi-simple, finite-dimensional Lie algebras.We extend the notion of Spin functor from finite-dimensional to symmetrizable Kac-Moody algebras, which requires a very delicate treatment. We introduce a certain category of orthogonal g-representations for which, surprisingly, the Spin functor gives a g-representation in Bernstein-Gelfand-Gelfand category O. Also, for an integrable representation, Spin produces an integrable representation. We give the formula for the character of Spin representation for the above category and work out the factorization results for an embedding of a finite-dimensional, semi-simple Lie algebra into its untwisted affine Lie algebra. Finally, we discuss the classification of those representations for which Spin is irreducible. 相似文献
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We show that a necessary condition for the existence of a universal finite dimensionally computable filter is that the Lie algebra $ naturally associated with the Zakai' equation, be finite dimensional at each point and that there exists a homomorphism from a Lie algebra of vectors fields onto.Conversely, we show that, if the signal is one dimensional and if S is infinite dimensional at each point of R, then only the constant functions are such the filter ntf can be realized as theimage of a diffusion. 相似文献
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设F是特征零的域,L是F上的带三角分解的李代数,L^-是相应的Loop代数.本文将定义L^-上赋值模的概念,并给出其不可约模的张量积是不可约模的等价条件. 相似文献
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This paper studies connected components of open subsemigroups of non-compact
semi-simple Lie groups by using control sets in the flag manifolds and their
coverings.
The concept of recurrent component is introduced and a method is given by
which their number can be computed. It is shown that the union of all
recurrent components is a semigroup. The idea of mid-reversibility comes up
to show that an open semigroup has just one semigroup component if the
identity belongs to its closure. A necessary and sufficient condition for
mid-reversibility is proved showing that e.g. in a complex group any open
semigroup is mid-reversible. 相似文献
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Ágota Figula 《Results in Mathematics》2006,49(1-2):45-79
In this paper we determine the at least 4-dimensional affine reductive homogeneous manifolds for an at most 9-dimensional
simple Lie group or an at most 6-dimensional semi-simple Lie group. Those reductive spaces among them which admit a sharply
transitive differentiable section yield local almost differentiable left A-loops. Using this we classify all global almost
differentiable left A-loops L having either a 6-dimensional semi-simple Lie group or the group
as the group topologically generated by their left translations. Moreover, we determine all at most 5-dimensional left A-loops
L with
as the group topologically generated by their left translations. 相似文献
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We prove that any noncocompact irreducible lattice in a higher rank real semi-simple Lie group contains a subgroup of finite index which is generated by three elements.A sizeable part of this paper forms the thesis of R. Sharma, submitted in April 2004 to the Tata Institute of Fundamental Research, Mumbai for the award of a PhD degree. 相似文献