共查询到20条相似文献,搜索用时 20 毫秒
1.
Ian M. Musson 《代数通讯》2013,41(10):3759-3777
If is a semisimple Lie algebra, we describe the prime factors of () that have enough finite dimensional modules. The proof depends on some combinatorial facts about the Weyl group which may be of independent interest. We also determine, which finite dimensional ()-modules are modules over a given prime factor. As an application we study finite dimensional modules over some rings of invariant differential operators arising from Howe duality. 相似文献
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In this paper, some irreducible graded modules with 1-dimensional homogeneous spaces over the Virasoro-like algebra and its q-analogs are constructed. The unitarizability of these modules, and the conditions under which two of such irreducible graded modules are ismorphic are determined. Some other kinds of irreducible graded modules with 1-dimensional homogeneous spaces over the Virasorolike algebra and its q-analogs are also given. 相似文献
3.
Susanne Danz 《代数通讯》2013,41(12):4521-4539
4.
We study some properties of generalized reduced Verma modules over ?-graded modular Lie superalgebras. Some properties of the generalized reduced Verma modules and coinduced modules are obtained. Moreover, invariant forms on the generalized reduced Verma modules are considered. In particular, for ?-graded modular Lie superalgebras of Cartan type we prove that generalized reduced Verma modules are isomorphic to mixed products of modules. 相似文献
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In this article,some modules over a loop Lie algebra associated to quantum plane are constructed.The isomorphism classes among these modules are also determined. 相似文献
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M. Grassi 《Journal of Algebra》1996,180(3):918
I first define Koszul modules, which are a generalization to arbitrary rank of complete intersections. After a study of some of their properties, it is proved that Gorenstein algebras of codimension one or two over a local or graded CM ring are Koszul modules, thus generalizing a well known statement for rank one modules. The general techniques used to describe Koszul modules are then used to obtain a structure theorem for Gorenstein algebras in codimension one and two, over a local or graded CM ring. 相似文献
9.
Guillaume Tomasini 《Comptes Rendus Mathematique》2010,348(9-10):509-512
In the study of simple modules over a simple complex Lie algebra, Bernstein, Gelfand and Gelfand introduced a category of modules which provides a natural setting for highest weight modules. In this note, we define a family of categories which generalizes the BGG category. We classify the simple modules for some of these categories. As a consequence we show that these categories are semisimple. 相似文献
10.
Steven E. Landsburg 《Journal of Pure and Applied Algebra》1981,21(3):261-277
In the first section of this paper, we prove several ‘Milnor-Mayer-Vietoris’-type patching theorems for projective modules. In the second section we apply these theorems to projective modules over polynomial rings and give some criteria for such modules to be extended. In the third section, the theorems are applied to the study of vector bundles over curves. 相似文献
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Higher Level Orderings on Modules 总被引:1,自引:0,他引:1
MinWU GuangXingZENG 《数学学报(英文版)》2005,21(2):279-288
The aim of this paper is to investigate higher level orderings on modules over commutative rings. On the basis of the theory of higher level orderings on fields and commutative rings, some results involving existence of higher level orderings are generalized to the category of modules over commutative rings. Moreover, a strict intersection theorem for higher level orderings on modules is established. 相似文献
13.
We describe some I-radicals in the categories of modules over semilocal rings. We give a characterization of rings over which the set of I-radicals coincides with the set of hereditary idempotent radicals. We prove that the lattices of I-radicals in the categories of modules over Morita-equivalent rings are isomorphic. 相似文献
14.
We introduce the notions of a four-angle Hopf quasimodule and an adjoint quasiaction over a Hopf quasigroup H in a symmetric monoidal category C.If H possesses an adjoint quasiaction,we show that symmetric Yetter-Drinfeld categories are trivial,and hence we obtain a braided monoidal category equivalence between the category of right Yetter-Drinfeld modules over H and the category of four-angle Hopf modules over H under some suitable conditions. 相似文献
15.
Strongly Gorenstein Flat Modules and Dimensions 总被引:1,自引:0,他引:1
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Punita Batra 《Journal of Pure and Applied Algebra》2011,215(7):1552-1568
Inspired by recent activities on Whittaker modules over various (Lie) algebras, we describe a general framework for the study of Lie algebra modules locally finite over a subalgebra. As a special case, we obtain a very general set-up for the study of Whittaker modules, which includes, in particular, Lie algebras with triangular decomposition and simple Lie algebras of Cartan type. We describe some basic properties of Whittaker modules, including a block decomposition of the category of Whittaker modules and certain properties of simple Whittaker modules under some rather mild assumptions. We establish a connection between our general set-up and the general set-up of Harish-Chandra subalgebras in the sense of Drozd, Futorny and Ovsienko. For Lie algebras with triangular decomposition, we construct a family of simple Whittaker modules (roughly depending on the choice of a pair of weights in the dual of the Cartan subalgebra), describe their annihilators, and formulate several classification conjectures. In particular, we construct some new simple Whittaker modules for the Virasoro algebra. Finally, we construct a series of simple Whittaker modules for the Lie algebra of derivations of the polynomial algebra, and consider several finite-dimensional examples, where we study the category of Whittaker modules over solvable Lie algebras and their relation to Koszul algebras. 相似文献
18.
Zeng Guangxing 《代数通讯》2013,41(12):5847-5856
The aim of this paper is to develop the study of modules in real algebra. By introducing two kinds of reality for modules over commutative rings, we establish some results on semireal modules and real modules. Our results involve real radicals of submodules and orderings on modules. 相似文献
19.
A module of a finite group over a finite field with a symmetric non-degenerate bilinear form which is invariant by the group action is called a symmetric module. In this paper, a characterization of indecomposable orthogonal decompositions of symmetric semisimple modules and a criterion for the hyperbolic symmetric modules are obtained, and some applications to the self-dual permutation codes are shown. 相似文献
20.
Francisco Raggi Jos Rí os Hugo Rinc n Rogelio Fern ndez-Alonso Carlos Signoret 《Journal of Pure and Applied Algebra》2004,190(1-3):251-265
We continue the study of the big lattice of preradicals over a ring. We consider several operators acting on this lattice, for instance the pseudocomplement, the annihilator and the totalizer, as well as some relations among them. Using some of these operators we give characterizations of V-rings, of rings that are a finite direct sum of injective hulls of simple modules, and of rings such that besides the latter condition have also the property that each pair of simple modules are homologically connected. 相似文献