共查询到20条相似文献,搜索用时 31 毫秒
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ABSTRACT Let ? be a complete set of Sylow subgroups of a finite group G, that is, ? contains exactly one and only one Sylow p-subgroup of G for each prime p. A subgroup H of a finite group G is said to be ?-permutable if H permutes with every member of ?. The purpose of this article is to study the influence of ?-permutability of all maximal subgroups of the Sylow subgroups of the generalized Fitting subgroup of some normal subgroup of a finite group G on the structure of G. Our results improve and extend the main results of Asaad (1998), Asaad and Heliel (2003), Asaad et al. (1991), Li et al. (2003), Ramadan (1992), and Srinivasan (1980). 相似文献
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Hannah Henker 《代数通讯》2013,41(3):876-889
We will generalize Skryabin's Freeness Theorem [11]to quasi-Hopf algebras. We will show that for a finite dimensional quasi-Hopf algebra H and a right coideal subalgebra K ? H all (H, K)-quasi Hopf bimodules are free K-modules, in particular, H is a free right and left K-module. 相似文献
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Daniel Larsson 《代数通讯》2013,41(12):4303-4318
In this article we apply a method devised in Hartwig, Larsson, and Silvestrov (2006) and Larsson and Silvestrov (2005a) to the simple 3-dimensional Lie algebra 𝔰𝔩2(𝔽). One of the main points of this deformation method is that the deformed algebra comes endowed with a canonical twisted Jacobi identity. We show in the present article that when our deformation scheme is applied to 𝔰𝔩2(𝔽) we can, by choosing parameters suitably, deform 𝔰𝔩2(𝔽) into the Heisenberg Lie algebra and some other 3-dimensional Lie algebras in addition to more exotic types of algebras, this being in stark contrast to the classical deformation schemes where 𝔰𝔩2(𝔽) is rigid. 相似文献
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Let H be a finite-dimensional and semisimple Hopf algebra over an algebraically closed field of characteristic 0 such that H has exactly one isomorphism class of simple modules that have not dimension 1. These Hopf algebras were the object of study in, for instance, [1] and [9]. In this paper we study this property in the context of certain abelian extensions of group algebras and give a group theoretical criterion for such Hopf algebras to be of the above type. We also give a classification result in a special case thereof. 相似文献
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Local Weyl modules were originally defined for affine Lie algebras by Chari and Pressley in [5]. In this paper we extend the notion of local Weyl modules for a Lie algebra 𝔤 ?A, where 𝔤 is any Kac–Moody algebra and A is any finitely generated commutative associative algebra with unit over ?, and prove a tensor product decomposition theorem which generalizes result in [2, 5]. 相似文献
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Yanhua Ren 《代数通讯》2013,41(5):1510-1518
By using the generating sequence and relations given by Ringel for his Ringel–Hall algebra in [8], we give a Gröbner–Shirshov basis for quantum group of type G 2. 相似文献
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Thomas Cassidy 《代数通讯》2013,41(9):3742-3752
Vatne [13] and Green and Marcos [9] have independently studied the Koszul-like homological properties of graded algebras that have defining relations in degree 2 and exactly one other degree. We contrast these two approaches, answer two questions posed by Green and Marcos, and find conditions that imply the corresponding Yoneda algebras are generated in the lowest possible degrees. 相似文献
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Let A be an artin algebra. We show that the bounded homotopy category of finitely generated right A-modules has Auslander–Reiten triangles. Two applications are given: (1) we provide an alternative proof of a theorem of Happel in [14]; (2) we prove that over a Gorenstein algebra, the bounded homotopy category of finitely generated Gorenstein projective (resp. injective) modules, admits Auslander–Reiten triangles, which improve a main result in [12]. 相似文献
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R. Taillefer 《代数通讯》2013,41(4):1415-1420
We compute explicitly the bialgebra cohomology of the duals of the generalized Taft algebras, which are noncommutative, noncocommutative finite-dimensional Hopf algebras. In order to do this, we use an identification of this cohomology with an Ext algebra (Taillefer, 2004a) and a result describing the Drinfeld double of the dual of a generalized Taft algebra up to Morita equivalence (Erdmann et al., 2006). 相似文献
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Iwan Praton 《代数通讯》2013,41(3):811-839
Generalized down-up algebras were first introduced in Cassidy and Shelton (2004). Their simple weight modules were classified in Cassidy and Shelton (2004) in the noetherian case, and in Praton (2007) in the non-noetherian case. Here we concentrate on non-noetherian down-up algebras. We show that almost all simple modules are weight modules. We also classify the corresponding primitive ideals. 相似文献
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Adam Hajduk 《代数通讯》2013,41(9):3236-3244
We introduce a concept generalizing classical degenerations of algebras (defined by structure constants) and Crawley-Boevey degenerations introduced in [3]. We prove that if A 0 is such a generalized degeneration of A 1 and the algebras have equal dimensions, then A 0 is a degeneration of A 1 in the classical sense. 相似文献
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Jonas Gonçalves Lopes 《代数通讯》2013,41(2):478-492
Given a partial action α of a group G on the group algebra FH, where H is a finite group and F is a field whose characteristic p divides the order of H, we investigate the associativity question of the partial crossed product FH*α G. If FH*α G is associative for any G and any α, then FH is called “strongly associative.” Using a result of Dokuchaev and Exel (2005) we characterize the strongly associative modular group algebras FH for several classes of groups H. 相似文献
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Andrew Dolphin 《代数通讯》2013,41(12):5141-5158
In this article, we present a decomposition theorem for unitary spaces over a central simple division algebra with involution in characteristic 2. This is a generalization of a decomposition result for quadratic forms in characteristic 2 from [4] and extends a generalization of the Witt decomposition theorem for nonsingular spaces in this setting to cover spaces that may be singular. 相似文献
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This article is a continuous work of [17], where the coauthors introduced the notion of 𝒢-FP-injective R-modules. In this article, we define a notion of 𝒢-FP-injective dimension for complexes over left coherent rings. To investigate the relationships between 𝒢-FP-injective dimension and FP-injective dimension for complexes, the complete cohomology group bases on FP-injectives is given. 相似文献
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Yuly Billig 《代数通讯》2018,46(8):3413-3429
We reprove the results of Jordan [18] and Siebert [30] and show that the Lie algebra of polynomial vector fields on an irreducible a?ne variety X is simple if and only if X is a smooth variety. Given proof is self-contained and does not depend on papers mentioned above. Besides, the structure of the module of polynomial functions on an irreducible smooth a?ne variety over the Lie algebra of vector fields is studied. Examples of Lie algebras of polynomial vector fields on an N-dimensional sphere, non-singular hyperelliptic curves and linear algebraic groups are considered. 相似文献
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Bangteng Xu 《代数通讯》2013,41(12):5249-5263
A problem that has been open for a long time is whether an automorphism of the center of the integral group ring of a finite group permutes the class sums. As a generalization, the similar problem for integral table algebras has also been studied in a few papers. In this paper we further the investigation of the problem for integral C-algebras and table algebras. We will first present some necessary and sufficient conditions under which an algebra isomorphism between integral C-algebras is monomial, and as an application, obtain a conceptual proof of the class sum correspondence theorem of group rings of finite groups. Then we prove that an algebra isomorphism compatible with degree maps between standard integral nilpotent table algebras over the ring of algebraic integers is exact. As a direct consequence, we get Hertweck's result [6] for finite nilpotent groups. An application to association schemes is also presented. 相似文献
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Mathieu Mansuy 《代数通讯》2018,46(4):1397-1419
We define integrable representations of quantum toroidal algebras of type A by tensor product, using the Drinfeld “coproduct.” This allows us to recover the vector representations recently introduced by Feigin–Jimbo–Miwa–Mukhin [7] and constructed by the author [21] as a subfamily of extremal loop weight modules. In addition we get new extremal loop weight modules as subquotients of tensor powers of vector representations. As an application we obtain finite-dimensional representations of quantum toroidal algebras by specializing the quantum parameter at roots of unity. 相似文献
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We define a notion of Morita equivalence between algebras with antiautomorphisms such that two equivalent algebras have the same category of sesquilinear forms. This generalizes the Morita equivalence of algebras with involutions defined by Fröhlich and Mc Evett [5], and their categories of ?-hermitian forms. For two Morita equivalent algebras with involution, with an additional technical property (which is true for central simple algebras), we define a new algebra with antiautomorphism, called the orthogonal sum, which generalizes the usual notion of orthogonal sum of forms. We explore the invariants of this sum. 相似文献