共查询到20条相似文献,搜索用时 15 毫秒
1.
We study cohomological induction for a pair $ {\left( {\mathfrak{g},\mathfrak{k}} \right)} $ , $ \mathfrak{g} $ being an infinitedimensional locally reductive Lie algebra and $ \mathfrak{k} \subset \mathfrak{g} $ being of the form $ \mathfrak{k}_{0} \subset C_{\mathfrak{g}} {\left( {\mathfrak{k}_{0} } \right)} $ , where $ \mathfrak{k}_{0} \subset \mathfrak{g} $ is a finite-dimensional reductive in $ \mathfrak{g} $ subalgebra and $ C_{\mathfrak{g}} {\left( {\mathfrak{k}_{0} } \right)} $ is the centralizer of $ \mathfrak{k}_{0} $ in $ \mathfrak{g} $ . We prove a general nonvanishing and $ \mathfrak{k} $ -finiteness theorem for the output. This yields, in particular, simple $ {\left( {\mathfrak{g},\mathfrak{k}} \right)} $ -modules of finite type over k which are analogs of the fundamental series of generalized Harish-Chandra modules constructed in [PZ1] and [PZ2]. We study explicit versions of the construction when $ \mathfrak{g} $ is a root-reductive or diagonal locally simple Lie algebra. 相似文献
2.
本文我们研究了两类$W$-型李代数$g(\lambda)$的Verma模的结构. 在一定条件下,我们决定了这些Verma模的可约性及相应的奇异向量. 相似文献
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Takahiko Furuya 《代数通讯》2013,41(8):2926-2942
Let Λ be a finite-dimensional (D, A)-stacked monomial algebra. In this article, we give necessary and sufficient conditions for the variety of a simple Λ-module to be nontrivial. This is then used to give structural information on the algebra Λ, as it is shown that if the variety of every simple module is nontrivial, then Λ is a D-Koszul monomial algebra. We also provide examples of (D, A)-stacked monomial algebras which are not self-injective but nevertheless satisfy the finite generation conditions (Fg1) and (Fg2) of [4], from which we can characterize all modules with trivial variety. 相似文献
6.
Andre Fonseca 《代数通讯》2013,41(9):3686-3694
7.
《Algebra Colloquium》2009,16(1):131-142
8.
In this paper we prove that there are no self-extensions of simple modules over restricted Lie algebras of Cartan type. The proof given by Andersen for classical Lie algebras not only uses the representation theory of the Lie algebra, but also representations of the corresponding reductive algebraic group. The proof presented in the paper follows in the same spirit by using the construction of a infinite-dimensional Hopf algebra D(G) u(
) containing u(
) as a normal Hopf subalgebra, and the representation theory of this algebra developed in our previous work. Finite-dimensional hyperalgebra analogs D(G
r
) u(
) have also been constructed, and the results are stated in this setting. 相似文献
9.
We study the relation between the cohomology of general linear and symmetric groups and their respective quantizations, using Schur algebras and standard homological techniques to build appropriate spectral sequences. As our methods fit inside a much more general context within the theory of finite-dimensional algebras, we develop our results first in that general setting, and then specialize to the above situations. From this we obtain new proofs of several known results in modular representation theory of symmetric groups. Moreover, we reduce certain questions about computing extensions for symmetric groups and Hecke algebras to questions about extensions for general linear groups and their quantizations. 相似文献
10.
Algebras and Representation Theory - For a smooth irreducible affine algebraic variety we study a class of gauge modules admitting compatible actions of both the algebra $mathcal {A}$ of functions... 相似文献
11.
Let G be a connected reductive algebraic group over an algebraically closed field of prime characteristic p and ?? be the Lie algebra of G. In this paper, we study the representations of ?? when p-character has standard Levi form. An Ext-transfer from the Ext-groups of induced ??-modules to its Levi subalgebras is obtained. Furthermore, we reduce the computation of the multiplicities of simple factors in baby Verma modules over ?? to its Levi subalgebras. 相似文献
12.
Paul Levy 《Journal of Algebra》2002,250(2):473
Let K be an algebraically closed field of positive characteristic and let G be a reductive group over K with Lie algebra
. This paper will show that under certain mild assumptions on G, the commuting variety
(
) is an irreducible algebraic variety. 相似文献
13.
Bin Wang 《Algebras and Representation Theory》2011,14(4):691-702
In this paper, we study Whittaker modules for graded Lie algebras over ℂ. We define Whittaker modules for a class of graded
Lie algebras and obtain a bijective correspondence between the set of isomorphism classes of Whittaker modules and the set
of ideals of a polynomial ring, parallel to a result from the classical setting and the case of the Virasoro algebra. As a
consequence of this, we obtain a classification of simple Whittaker modules for such algebras. Also, we discuss some concrete
algebras as examples. 相似文献
14.
孟道骥等对完备李代数作了系统的研究并已获得很多基本和重要的结果。本文给出完备李群与完备李代数的某些关系。 相似文献
15.
Behrouz Edalatzadeh 《代数通讯》2013,41(8):3366-3380
In this paper, we introduce the concept of capability for crossed modules of Lie algebras, which is a generalization of capability in Lie algebras and groups. By using a special central ideal of a crossed module, we give a sufficient condition for the capability of a crossed module of Lie algebras. Also, we will extend the five-term exact sequence on homology of crossed modules of Lie algebras one term further and study the connection between the capability of crossed modules and this sequence. Finally, we study the relation between the capability and the center of a cover of a crossed module. 相似文献
16.
Ivan Marin 《代数通讯》2013,41(7):2572-2584
We consider the natural Lie algebra structure on the (associative) group algebra of a finite group G, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a decomposition in simple factors of these Lie algebras, in terms of the ordinary representations of G. 相似文献
17.
Let
be an untwisted affine Kac–Moody algebra and MJ() a Verma-type module for
with J-highest weight P. We construct quantum Verma-type modules MJq() over the quantum group
, investigate their properties and show that MJq() is a true quantum deformation of MJ() in the sense that the weight structure is preserved under the deformation. We also analyze the submodule structure of quantum Verma-type modules.
Presented by A. VerschorenMathematics Subject Classifications (2000) 17B37, 17B67, 81R50.The first author is a Regular Associate of the ICTP. The third author was supported in part by a Faculty Research Grant from St. Lawrence University. 相似文献
18.
KAREL Dekimpe 《Compositio Mathematica》2000,121(2):183-204
In this paper, we study polynomial structures by starting on the Lie algebra level, thenpassing to Lie groups to finally arrive at the polycyclic-by-finite group level. To be more precise,we first show how a general solvable Lie algebra can be decomposed into a sum of two nilpotentsubalgebras. Using this result, we construct, for any simply connected, connected solvable Lie groupG of dim n, a simply transitive action on R
n which is polynomial and of degree n3. Finally, we show the existence of a polynomial structure on any polycyclic-by-finite group , which is of degree h()3 on almost the entire group (h () being the Hirsch length of ). 相似文献
19.
本文首先给出广义扭仿射李代数的概念;然后讨论这种李代数的不可约模H的性质;特别是给出了H的一个自然阶化分解;通过研究扭李代数g的流表示,证明关于扭流的换位关系式;最后证明作用在不可约模上的一类算子的局部幂零性.这一结果对研究共形块空间的广义扭仿射李代数模的实现起着基本的作用. 相似文献
20.
In this paper,we study a class of soluble Lie algebras with variety relations that the commutator of m and n is zero.The aim of the paper is to consider the relationship between the Lie algebra L with ... 相似文献