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1.
In this article we first study an equivariant cyclic cohomology for weak H-module agebras over a weak Hopf algebra H with a bijective antipode. Then we define an equivariant K-theory for weak quantum Yetter–Drinfeld algebras over H and establish a generalized Connes' pairing between the equivariant cyclic cohomology and the equivariant K-theory. As an application we consider our theory for groupoids. 相似文献
2.
The set of pure-injective cotilting modules over an artin algebra is shown to have a monoid structure. This monoid structure
does not restrict down to a monoid structure on the finitely generated cotilting modules in general, but it does whenever
the algebra is of finite representation type. Pure-injective cotilting modules are also constructed from any set of finitely
generated cotilting modules with bounded injective dimension.
Presented by Y. Drozd
Mathematics Subject Classifications (2000) 16G10, 16P20, 16E30. 相似文献
3.
引入了弱d-Koszul模,它是d-Koszul模的一种自然推广.设A是d-Koszul代数,M是有限生成的分次A-模,则M是弱d-Koszul模当且仅当M具有子模滤:0(?)U0(?)U1(?)…(?)Up=M,使得所有的A-模Ui/Ui-1是d-Koszul模.设M为一个弱d-Koszul模,则作为分次ExtA*(A0,A0)-模,其Koszul对偶:ε(M)=ExtA*(M,A0)是由0次生成的. 相似文献
4.
Christian Böhning 《代数通讯》2013,41(6):2014-2022
5.
Iwan Praton 《代数通讯》2013,41(1):325-337
We classify all simple weight modules of non-Noetherian generalized down-up algebras. 相似文献
6.
For complex Lie algebra sl(n, C) we study the submodule structure of generalized Verma modules induced from generic Gelfand-Zetlin modules over some subalgebra of type sl(k, C). We obtain necessary and sufficient conditions for the existence of a submodule generalizing the Bernstein-Gelfand-Gelfand theorem for Verma modules. 相似文献
7.
8.
证明存在Hammock位于有限表示型代数A上BB-倾斜模T_A诱导的AR-箭图上和代数B=End(T_A)的AR-箭图上,并用Hammock对BB-倾斜模T_A进行刻画. 相似文献
9.
《代数通讯》2013,41(9):2921-2940
ABSTRACT An equivalent version of the Generalized Nakayama Conjecture states that any projective almost complete tilting module admits a finite number of non-isomorphic indecomposable complements. Motivated by this connection, we investigate the number of possible complements of projective almost complete tilting modules for some particular classes of Artin algebras, namely monomial algebras and algebras with exactly two simple modules. 相似文献
10.
We give a characterization of indecomposable exceptional modules over finite dimensional gentle algebras. As an application, we study gentle algebras arising from an unpunctured surface and show that a class of indecomposable modules related to curves without self-intersections, as exceptional modules, are uniquely determined by their dimension vectors. 相似文献
11.
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
12.
Husney Parvez Sarwar 《代数通讯》2013,41(5):2256-2263
(1) Let R be a 1-dimensional commutative Noetherian anodal ring with finite seminormalization and M a commutative cancellative torsion-free monoid. Let P be a projective R[M]-module of rank r. Then P ? ∧rP ⊕ R[M]r?1.(2) Murthy and Pedrini [11] proved K0 homotopy invariance of polynomial extension of some affine normal surfaces. We extend this result to a monoid extension (see 1.5). 相似文献
13.
Jacob Greenstein 《Algebras and Representation Theory》2003,6(2):119-137
After V. Chari and A. Pressley, a simple integrable module with finite-dimensional weight spaces over an affine Lie algebra is either a standard module (highest or lowest weight), in which case its formal character is given by the famous Weyl–Kac formula, or a subquotient of a tensor product of loop modules. In this paper we compute formal characters of generic simple integrable modules of the latter type. 相似文献
14.
A. Joseph 《Algebras and Representation Theory》2000,3(2):131-149
This paper studies a class of simple integrable modules for an affine Lie algebras which are closely related to the finite-dimensional modules studied by V. Chari and A. Pressley, except that the Euler element is assumed to act. They are infinite-dimensional; but are shown to have finite-dimensional weight spaces. It is conjectured that any simple integrable module with a zero weight space belongs to this class and their classification is given. The main interest in studying such modules is that they may occur in the endomorphism rings of highest weight modules whilst those of Chari and Pressley in general do not. Their character theory is also more complicated. 相似文献
15.
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
16.
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
17.
18.
Indah Emilia Wijayanti 《代数通讯》2013,41(4):1308-1333
Many observations about coalgebras were inspired by comparable situations for algebras. Despite the prominent role of prime algebras, the theory of a corresponding notion for coalgebras was not well understood so far. Coalgebras C over fields may be called coprime provided the dual algebra C* is prime. This definition, however, is not intrinsic—it strongly depends on the base ring being a field. The purpose of the article is to provide a better understanding of related notions for coalgebras over commutative rings by employing traditional methods from (co)module theory, in particular (pre)torsion theory. Dualizing classical primeness condition, coprimeness can be defined for modules and algebras. These notions are developed for modules and then applied to comodules. We consider prime and coprime, fully prime and fully coprime, strongly prime and strongly coprime modules and comodules. In particular, we obtain various characterisations of prime and coprime coalgebras over rings and fields. 相似文献
19.
Izuru Mori 《代数通讯》2013,41(12):4659-4677
Let A be a Frobenius Koszul algebra such that its Koszul dual A ! is a quantum polynomial algebra. Co-point modules over A were defined as dual notion of point modules over A ! with respect to the Koszul duality. In this article, we will see that various important functors between module categories over A used in representation theory of finite dimensional algebras send co-point modules to co-point modules. As a consequence, we will show that if (E, σ) is a geometric pair associated to A !, then the map σ:E → E is an automorphism of the point scheme E of A !, so that there is a bijection between isomorphism classes of left point modules over A ! and those of right point modules over A !. 相似文献
20.
Let C be a faithfully balanced selforthogonal module over an Artin algebra R. We introduce the notion of n-C-star modules, which is a common generalization of n-star modules and n-C-tilting modules. We extend some characterizations of n-star modules to this context and prove that n-C-tilting modules are precisely n-C-star modules n-C-presenting all the injectives. 相似文献