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1.
A= Z[v]Ω,Ω Z[v]的由-1和奇p生成的理想. U是 A上的量子代数.令 фp是 p次分圆多项式, B= A/(фp),г 是商代数 B关于理想(ζ— 1)的完备化,式中ζ是p次本原根.对人 λ∈ X+, Mг(λ)表首权为λ的不可分解 Uг-Tiltins模(称为主 Uг模).本文给出了量子群主 Uг模的张量积定理.对 p≥ 2(h-1),在 p2室中描述了量子群主 Uг模好滤过滤过商之首权的分布状态及其滤过重数作为例子,对秩1型和 A2型的量子群情形给出了 P2室中一般位置室主 Uг模好滤过的分解模式.  相似文献   

2.
在弱Hopf群余代数情形中,讨论了一簇从弱Doi-Hopf群模范畴到某个代数上的模范畴忘却函子的可分性,诱导出弱Doi-Hopf群模数据的正规化积分概念,证明了正规化积分存在性是忘却函子可分的判别准则.所得结果在弱量子Yetter-Drinfel'd群模范畴及弱相对Hopf群模范畴中有应用价值.  相似文献   

3.
按环路α-连对角占优阵及应用   总被引:4,自引:0,他引:4  
李竹香  逄明贤 《计算数学》2001,23(3):271-278
1.引言与记号 利用矩阵的对角占优性研究矩阵的特征值分布和非奇H矩阵的判定,是数值代数的重要课题.[1]-[4]给出了利用 Ostrowski定理及连对角占优性判定非奇 H-矩阵的最新成果.本文引入按环路α-连对角占优概念,给出了非奇H-矩阵的判定条件及等价表征,简化了计算,改进与推广了[1]-[9]的相应结果. 设A=.Γ(A)表 A的方向图,其顶点集及弧集分别记作 V(A)及 E(A),eij表从顶点i到顶点 j的弧, C(A)表 Γ(A)中非平凡环路集合.对任意固定 α E[0,1]还记*k伪行、列足…  相似文献   

4.
本文通过函子T=-ARnA讨论了倾斜A 模与倾斜RnA 模的重要联系,推广了[1]的主要结果;讨论了倾斜RnA 模TX与倾斜A 模导出的挠理论在相同性和分裂性等方面的关系.  相似文献   

5.
实二次代数整数环上的正定幺模格的分类   总被引:5,自引:0,他引:5  
王瑞卿 《数学学报》2002,45(1):203-208
推广了Kneser的邻格方法,研究了Z[/d]  上的秩4n判别式1的正定幺模种的邻格性质,完成了Z[/3]上秩4的正定幺模格的分类.  相似文献   

6.
Fuzzy代数与Fuzzy商代数   总被引:5,自引:0,他引:5  
本文更深入地讨论了Fuzzy代数,Fuzzy理想的性质,定义了Fuzzy商代数,并证明了代数Y关于代数Z的同态f-1[Oz]的Fuzzy商代数与代数Z同构等性质。  相似文献   

7.
量子群主Tilting模的张量积及其滤过   总被引:1,自引:0,他引:1  
柏元淮 《数学年刊A辑》2001,22(2):229-236
A=z[υ]Ω,Ω是Z[υ]的由υ-1和奇素数p生成的理想.U是A上的量子代数.令φp是p次分圆多项式,B=A/(φp),Γ是商代数B关于理想(ξ-1)的完备化,式中ξ是p次本原根.对λ∈X+,Mr(λ)表首权为λ的不可分解Uг-Tilting模(称为主Ur模).本文给出了量子群主Ur模的张量积定理.对p≥2(h-1),在p2室中描述了量子群主Ur模好滤过滤过商之首权的分布状态及其滤过重数.作为例子,对秩1型和A2型的量子群情形给出了p2室中一般位置室主Ur模好滤过的分解模式.  相似文献   

8.
查建国 《数学杂志》1995,15(3):263-272
在本文中我们推广了Misra^[1]的结果,利用Lepowsky和Wilson引进的Z-代数来研究标准模的结构,对仿射李代数A^(1)2n我们能够确定某些水平为2的标准模的真空空间的一组基,本文的结果同Misra^[5]的结果完全不同。  相似文献   

9.
分次Morita对偶,Morita对偶与Smash积   总被引:1,自引:0,他引:1  
张圣贵 《数学学报》1994,37(6):756-761
设C和r都是群,是G-型分次环,是Γ-型分次环.是双分次模,R#G是R的Smash积,A#Γ是A的Smash积。令W=(_gU_(σ-1))_(g,σ)即(g,σ)位置取_gU_(σ-1)的元素的|G|×|Γ|矩阵的全体组成的集合,且每个矩阵的每行和每列的非零元只有有限个,按矩阵运算,W构成(R#6,A#Γ)双模。则_RU_A定义了一个分次Morita对偶当且仅当_(R#G)W_(A#Γ)定义了一个Morita对偶。  相似文献   

10.
在本文中我们推广了Misra ̄[1]的结果,利用Lepowsky和Wilson引进的Z-代数来研究标准模的结构,对仿射李代数A我们能够确定某些水平为2的标准模的真空空间的一组基,本文的结果同Misra ̄[5]的结果完全不同。  相似文献   

11.
柏元淮 《数学学报》1997,40(2):301-307
令M是Z[v]的由v-1和奇素数p生成的理想,U是A=Z[v]M上相伴于对称Cartan矩阵的量子代数.k是特征为零的代数闭域,A→k(v(?)ξ)是环同态.U_k=U(?)_Ak,u_k是U_k的无穷小量子代数.令ξ是1的p次本原根.本文证明了:若有限维可积U_k模M,V中至少有一个是内射模,或者M,V中有一个模作为u_k模是平凡的,则有U_k模同构M(?)V≌V(?)M.我们还证明了:若有限维可积U_k模V作为u_k模是不可分解的,有限维可积U_k模M是不可分解的,且M|_(uk)是平凡的,则V(?)M是不可分解U_k模.令V和M是有限维可积U_k模,作为u_k模是同构的且具有单基座,本文证明V和M作为U_k模也是同构的.由此得到:不可分解内射u_k模提升为U_k模是唯一的.  相似文献   

12.
Global and local Weyl modules were introduced via generators and relations in the context of affine Lie algebras in [CP2] and were motivated by representations of quantum affine algebras. In [FL] a more general case was considered by replacing the polynomial ring with the coordinate ring of an algebraic variety and partial results analogous to those in [CP2] were obtained. In this paper we show that there is a natural definition of the local and global Weyl modules via homological properties. This characterization allows us to define the Weyl functor from the category of left modules of a commutative algebra to the category of modules for a simple Lie algebra. As an application we are able to understand the relationships of these functors to tensor products, generalizing results in [CP2] and [FL]. We also analyze the fundamental Weyl modules and show that, unlike the case of the affine Lie algebras, the Weyl functors need not be left exact.  相似文献   

13.
《Quaestiones Mathematicae》2013,36(4):303-312
Abstract

This paper deals with projectives (in the sense of K.A.Hardie [5] relative to a right adjoint functor U: A → K. We answer the question, raised by R.-E. Hoffmann [6] p. 135, of knowing under what conditions there exists an equivalence between Proj u and Proj Ur, induced by the comparison functor Φ: A → KT, where T denotes the monad induced by U. In the case, that U is an algebraic functor we also give necessary and sufficient conditions for the re gular projective objects to coincide with the U-projectives. Finally, we delineate how these results nay be applied in certain familiar situations.  相似文献   

14.
Quantum homogeneous supervector bundles arising from the quantum general linear supergoup are studied. The space of holomorphic sections is promoted to a left exact covariant functor from a category of modules over a quantum parabolic sub-supergroup to the category of locally finite modules of the quantum general linear supergroup. The right derived functors of this functor provides a form of Dolbeault cohomology for quantum homogeneous supervector bundles. We explicitly compute the cohomology groups, which are given in terms of well understood modules over the quantized universal enveloping algebra of the general linear superalgebra.  相似文献   

15.
This paper is the sequel of a previous one [2] where we extended the Tannaka-Krein duality results to the non-commutative situation, i.e. to ‘quantum groupoids’. Here we extend those results to the quasi-monoidal situation, corresponding to ‘quasi-quantum groupoids’ as defined in [3] (‘quasi-’ stands for quasi-associativity a la Drinfeld). More precisely, let B be a commutative algebra over a field k. Given a tensor autonomous category τ,. we define the notion of a quasi-fibre functor ω:τ-proj B (here, ‘quasi-’ means without compatibility to associativity constraints). On the other hand, we define the notion of a transitive quasi-quantum groupoid over B. We then show that the category of tensor autonomous categories equipped with a quasi-fibre functor (with suitable morphisms), is equivalent to the category of transitive quasi-quantum groupoids (5.4.2)

Moreover, we classify quasi-fibre functors for a semisimple tensor autonomous category (6.1.2), and give a few examples : a family of quantum groups having the same tensor category of representations as Sl2(C), but with non-isornorphic underlying coalgebras, constructed by means of an R-matrix introduced by Gurevich ([9]) in a manner suggested to the author by Lyubashenko (6.2.1 and 6.2.2), and quasi-quantum groups which cannot be obtained from quantum groups by a Drinfeld twist (6.2.1)  相似文献   

16.
Given a quiver, a fixed dimension vector, and a positive integer n, we construct a functor from the category of D-modules on the space of representations of the quiver to the category of modules over a corresponding Gan–Ginzburg algebra of rank n. When the quiver is affine Dynkin, we obtain an explicit construction of representations of the corresponding wreath product symplectic reflection algebra of rank n. When the quiver is star-shaped, but not finite Dynkin, we use this functor to obtain a Lie-theoretic construction of representations of a “spherical” subalgebra of the Gan–Ginzburg algebra isomorphic to a rational generalized double affine Hecke algebra of rank n. Our functors are a generalization of the type A and type BC functors from [1] and [4], respectively.  相似文献   

17.
This paper is a continuation of [EK]. We show that the quantization procedure of [EK] is given by universal acyclic formulas and defines a functor from the category of Lie bialgebras to the category of quantized universal enveloping algebras. We also show that this functor defines an equivalence between the category of Lie bialgebras over k [[h]] and the category of quantized universal enveloping (QUE) algebras.  相似文献   

18.
Alain Bruguières 《代数通讯》2013,41(14):5817-5860
Inspired by a recent paper by Deligne [2], we extend the Tannaka-Krein duility results (over a field) to the non-commutative situation. To be precise, we establish a 1-1 corresponde:ice between ‘tensorial autonomous categories’ equipped with a ‘fibre functor’ (i. e. tannakian categories without the commutativity condition on the tensor product), and ‘quantum groupoids’ (as defined by Maltsiniotis, [9]) which are ‘transitive’ (7.1.). When the base field is perfect, a quantum groupoid over Spec B is transitive iff it is projective and faithfully fiat over B? k B. Moreover, the fibre functor is unique up to ‘quantum isomorphism’ (7.6.). Actually, we show Tannaka-Krein duality results in the more general setting where there is no monoidal structure on the category (and the functor); the algebraic object corresponding to such a category is a ‘semi-transitive’ coalgebroid (5.2. and 5.8.).  相似文献   

19.
In this paper we discuss the “Factorization phenomenon” which occurs when a representation of a Lie algebra is restricted to a subalgebra, and the result factors into a tensor product of smaller representations of the subalgebra. We analyze this phenomenon for symmetrizable Kac-Moody algebras (including finite-dimensional, semi-simple Lie algebras). We present a few factorization results for a general embedding of a symmetrizable Kac-Moody algebra into another and provide an algebraic explanation for such a phenomenon using Spin construction. We also give some application of these results for semi-simple, finite-dimensional Lie algebras.We extend the notion of Spin functor from finite-dimensional to symmetrizable Kac-Moody algebras, which requires a very delicate treatment. We introduce a certain category of orthogonal g-representations for which, surprisingly, the Spin functor gives a g-representation in Bernstein-Gelfand-Gelfand category O. Also, for an integrable representation, Spin produces an integrable representation. We give the formula for the character of Spin representation for the above category and work out the factorization results for an embedding of a finite-dimensional, semi-simple Lie algebra into its untwisted affine Lie algebra. Finally, we discuss the classification of those representations for which Spin is irreducible.  相似文献   

20.
n级三角矩阵环上的模范畴和同调特征   总被引:1,自引:0,他引:1  
史美华  李方 《数学学报》2006,49(1):215-224
本文给出了n级三角矩阵环Гn的定义.证明了n级三角矩阵代数Гn上的有限生成模范畴mod Гn与范畴Гn(?)等价,得到了诸如Гn的Jacobson根,Гn(?)的不可分解投射对象的形式及Гn的整体维数等性质.  相似文献   

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