共查询到20条相似文献,搜索用时 93 毫秒
1.
近十年来,特别是近几年完备Lie代数的研究取得了许多进展,本文分以下六个方面介绍这一领域的研究状况,0)引言;1)完备Lie代数的分解和唯一性;2)一些完备Lie代数。3)可解完备Lie代数;4)完备Lie代数的极大环面子代数,Killing型及结构;5)一些公开问题。 相似文献
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本文在三角Hopf代数表示范畴上系统地研究了Lie余代数,在此范畴上 的Lie余代数与Hopf代数之间建立了重要的联系.主要给出了Lie余代数的余包络 余代数的结构.所得结果自然是关于Lie代数的对偶结果,推广了 Sweedler M. E., Gurevich D.I., Michaelis W.和 Maiid S.等人的结果. 相似文献
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本文在三角Hopf代数表示范畴上系统地研究了Lie余代数,在此范畴上 的Lie余代数与Hopf代数之间建立了重要的联系.主要给出了Lie余代数的余包络 余代数的结构.所得结果自然是关于Lie代数的对偶结果,推广了 Sweedler M. E., Gurevich D.I., Michaelis W.和 Maiid S.等人的结果. 相似文献
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设α是域F上的结合超代数满足[α,α]=a或a=F.证明了当m+n>1时,H2(glm|n(α),F)≌HC1(a,F).定义了一大类广义微分算子李超代数,作为W-无穷代数W∞(glN)的推广.确定了这些李超代数的2-上循环.同时给出了矩阵量子微分算子李超代数的2-上同调群. 相似文献
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设α是域F上的结合超代数满足[α,α]=α或α=F.证明了当m n>1时,H2(glm|n(α),F)(?)HC1(α,F).定义了一大类广义微分算子李超代数,作为W-无穷代数W∞(glN)的推广.确定了这些李超代数的2-上循环.同时给出了矩阵量子微分算子李超代数的2-上同调群. 相似文献
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王栓宏 《数学年刊A辑(中文版)》2000,(5)
在 Yetter-Drinfel’d范畴中,本文研究了ρ-Lie代数的可解理想结构,得到了:如果L是一个 H-单的 ρ-Lie代数而且 V [L,L]ρ是[L,L]ρ的一个 ρ-Lie理想满足 V≠[L,L]ρ那么 V是[L,L]ρ的一个可解ρ-Lie子代数. 相似文献
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In this paper, we give a complete classification of irreducible Harish-Chandra modules for any generalized Heisenberg-Virasoro algebra. In particular, we present a simpler and more conceptual proof of the classification of irreducible Harish-Chandra modules over the classical Heisenberg-Virasoro algebra, which was first obtained by Rencai Lu and Kaiming Zhao in [LZ1]. Our methods are based on the ideas of polynomial modules from [B1, BB]. 相似文献
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Xu Xiang 《数学学报(英文版)》1997,13(2):161-168
In this paper we study the pointed representations of the Virasoro algebra. We show that unitary irreducible pointed representations
of the Virasoro algebra are Harish-Chandra representations, thus they either are of highest or lowest weights or have all
weight spaces of dimension 1. Further, we prove that unitary irreducible weight representations of Virasoro superalgebras
are either of highest weights or of lowest weights, hence they are also Harish-Chandra representations.
This work was supported by CNSF 相似文献
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It is shown that the support of an irreducible weight module over the SchrSdinger-Virasoro Lie algebra with an infinite-dimensional weight space coincides with the weight lattice, and all nontrivial weight spaces of such a module are infinite-dimensional. As a by-product, it is obtained that every simple weight module over Lie algebra of this type with a nontrivial finite-dimensional weight space is a Harish-Chandra module. 相似文献
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This paper constructs a class of Harish-Chandra modules with multiplicity ≤1 of the two parameter deformation of Virasoro algebra and proves a classification theorem. 相似文献
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In the present paper, we study the nonzero level Harish-Chandra modules for the Virasoro-like algebra. We prove that a nonzero level Harish-Chandra module of the Virasoro-like algebra is a generalized highest weight (GHW for short) module. Then we prove that a GHW module of the Virasoro-like algebra is induced from an irreducible module of a Heisenberg subalgebra. 相似文献
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Chen Zhonghu 《数学年刊B辑(英文版)》1995,16(1):63-74
ONTHEHARISH-CHANDRAHOMOMORPHISMFORTHECHEVALLEYGROUPSOVERP-ADICFIELD¥CHENZHONGHU(DepartmentofMathematics,XiangtanUniversitytXi... 相似文献
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We propose a notion of algebra of twisted chiral differential operators over algebraic manifolds with vanishing 1st Pontrjagin class. We show that such algebras possess
families of modules depending on infinitely many complex parameters, which we classify in terms of the corresponding algebra
of twisted differential operators. If the underlying manifold is a flag manifold, our construction recovers modules over an
affine Lie algebra parameterized by opers over the Langlands dual Lie algebra. The spaces of global sections of “smallest”
such modules are irreducible
[^(\mathfrakg)]{{\hat{{\mathfrak{g}}}}} -modules, and all irreducible
\mathfrakg{{\mathfrak{g}}} -integrable
[^(\mathfrakg)]{{\hat{{\mathfrak{g}}}}} -modules at the critical level arise in this way. 相似文献
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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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Alexander V. Karabegov 《Transactions of the American Mathematical Society》1998,350(4):1467-1479
We show that the theory of spherical Harish-Chandra modules naturally gives rise to Berezin's symbol quantization on generalized flag manifolds. It provides constructions of symbol algebras and of their representations for covariant and contravariant symbols, and also for symbols which so far have no explicit definition. For all these symbol algebras we give a general proof of the correspondence principle.
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We compute the cohomology of modules over the algebra of twisted chiral differential operators over the flag manifold. This is applied to (1) finding the character of G-integrable irreducible highest weight modules over the affine Lie algebra at the critical level, and (2) computing a certain elliptic genus of the flag manifold. The main tool is a result that interprets the Drinfeld–Sokolov reduction as a derived functor. 相似文献