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The first cohomology group of generalized loop Virasoro algebras with coefficients
in the tensor product of its adjoint module is shown to be trivial. The result is used
to prove that Lie bialgebra structures on generalized loop Virasoro algebras are coboundary
triangular. The authors generalize the results to generalized map Virasoro algebras. 相似文献
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给出了Virasoro代数的一类一致有界不可分解权模的分类,即分类了这样的不可分解模,其合成因子或者都是中间模A_(0,0)的合成因子,或者都同构于中间模A_(a,b)(其中a(?)Z或b≠0,1). 相似文献
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In this article, we study the structure theory of a class of generalized loop Virasoro algebras. In particular, the derivation algebras, the automorphism groups, and the second cohomology groups of generalized loop centerless Virasoro algebras are determined. 相似文献
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Jia Yuting 《东北数学》1997,(1)
OntheGeneralizedVirasoro┐likeAlgebrasJiaYuting(贾雨亭)(DepartmentofMathematics,HebeiTeachersUniversity,Shijiazhuang,050016)Zhang... 相似文献
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In this paper, we study the structure theory of a class of not-finitely graded Lie algebras related to generalized Virasoro algebras. In particular, the derivation algebras, the automorphism groups and the second cohomology groups of these Lie algebras are determined. 相似文献
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Xian-Dong Wang 《代数通讯》2013,41(2):415-424
ABSTRACT Given a field F with characteristic zero, a free Abelian group G with rank two, and a total order ? on G which is compatible with the addition, we define Verma modules M([ddot], ?) over the generalized Block algebra B(b (1), b (2)) with b (1), b (2) ∈ F. The irreducibility of the module M([ddot], ?) is completely determined in this article. 相似文献
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Following analogous constructions for Lie algebras, we define Whittaker modules and Whittaker categories for finite-dimensional simple Lie superalgebras. Results include a decomposition of Whittaker categories for a Lie superalgebra according to the action of an appropriate sub-superalgebra; and, for basic classical Lie superalgebras of type I, the construction of Whittaker modules from Whittaker modules for the even part. 相似文献
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Let L be the derivation Lie algebra of C[t±11,t±12].Given a triangle decomposition L=L~+⊕h⊕L~-,we define a nonsingular Lie algebra homomorphism ψ:L~+→C and the universal Whittaker L-module W_ψ of type ψ.We obtain all Whittaker vectors and submodules of W_ψ.Moreover,all simple Whittaker L-modules of type ψ are determined. 相似文献
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对任意的仿射李代数■,作者构造了一类水平为零的imaginary Whittaker ■模.同时证明了这类模在某些给定条件下是单的. 相似文献
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In this paper, we study Whittaker modules for a Lie algebra of Block type. We define Whittaker modules and under some conditions,
obtain a bijective correspondence between the set of isomorphism classes of Whittaker modules over this algebra and the set
of ideals of a polynomial ring, parallel to a result from the classical setting and the case of the Virasoro algebra. 相似文献
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Paula A. A. B. Carvalho 《代数通讯》2013,41(5):1622-1646
A generalization of down-up algebras was introduced by Cassidy and Shelton (2004), the so-called “generalized down-up algebras”. We describe the automorphism group of conformal Noetherian generalized down-up algebras L(f, r, s, γ) such that r is not a root of unity, listing explicitly the elements of the group. In the last section, we apply these results to Noetherian down-up algebras, thus obtaining a characterization of the automorphism group of Noetherian down-up algebras A(α, β, γ) for which the roots of the polynomial X 2 ? α X ? β are not both roots of unity. 相似文献
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《代数通讯》2013,41(9):3581-3608
Abstract We define generalized Virasoro operators acting on a Fock space V(Γ). These generalize the standard construction of Virasoro operators. By using the Jacobi Identity we compute the commutators of these operators. These operators result in an abelian extension of the toroidal Lie algebra. We explicitly describe the abelian extension. 相似文献
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Kenji Nishida 《Algebras and Representation Theory》2002,5(2):137-147
We provide a criterion for a -bimodule to be a dualizing module, where is an order over a commutative Gorenstein complete local domain of dim R=1. Using this criterion, we give examples of dualizing modules which are neither isomorphic to nor a dual of . Thus we can also give such examples over an Artin algebra by modulo a nonzerodivisor. 相似文献
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设g为特征为0的二次闭域上的Virasoro代数。本文决定了H^1(g,M(4,1)),H^2(g,M(4,2))及H^2(g,ML)的结构,其中M(4,1),M(4,2)为两类基本Harish-Chandra模,ML为无常数项单变量Laurent多项式。 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