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1.
斜群代数与平凡扩张的表示维数   总被引:1,自引:0,他引:1  
设A是域k上的一个有限维自入射代数,G是一个有限群,且G的阶在A中可逆,A*G是斜群代数,T(A)是平凡扩张代数,∧V是外代数.本文证明了A的稳定范畴与A*G的稳定范畴的三角维数相等,得到了∧V*G及T(∧V*G)的表示维数.  相似文献   

2.
设A是域k上的有限维代数,(Q,I)是带关系的箭图,令Λ=AkkQ/I.Λ的模范畴Λ-Mod及有限生成模范畴Λ-mod分别与(Q,I)在A上的表示范畴Rep(Q,I,A)及有限维表示范畴rep(Q,I,A)等价.给出了范畴rep(A_3,I,A)中Gorenstein投射模的具体构造,其中(A_3,I)=3α→2β→1,I=βα.在此基础上,给出了代数A是自入射代数的一个充分必要条件.  相似文献   

3.
O.Bratteli推广J.Glimm的一致超有限(UHF)代数,而引入(AF)代表.虽然Bratteli也给出(AF)代数的同构定理,但这个定理使用起来并不容易.G.A.Elliott引入维数群的概念,在[3,4]中,均谈到这样的稳定同构定理: 设A,B是(AF)代数,G(A),G(B)分别是A,B的维数群,则G(A)序同构于G(B),必须且只须,A K*同构于B K,这里K是可分Hilbert空间中全连续算子全体的c~*-代数.  相似文献   

4.
令A为诺特基本k-代数,设J为其Jacobson根且半单代数A/J同构于有限个k的直积.证明了如果A是AS-Gorenstein代数,则其Yoneda代数Ext*A(A/J,A/J)是Frobenius代数;如果A的内射维数injdimAA=d,则函子ExtdA(-,A)是可表示的.  相似文献   

5.
侯波  徐运阁 《数学学报》2008,51(2):241-252
设Λ是特征不整除n的域k上的二元外代数,■是Λ的Zn-Galois覆盖代数.首先构造了■的极小投射双模分解,并由此清晰地计算了■的各阶Hochschild同调和上同调群的维数;并且在域的特征为零时,计算了■的循环同调群的维数.  相似文献   

6.
讨论半单Hopf代数上经cleft扩张后的代数表示的不变性质.首先,解释了cleft扩张的概念,并给出cleft扩张和交叉积之间的联系(交叉积是解决问题的基本方法).然后,利用这些关系证明了:当k是代数闭域,H是一个有限维的半单k代数时,对一个有限维k代数,其H-cleft扩张下的代数表示型是不变的.另一方面证明了:当k是任意域,H是一个有限维的半单k-Hopf代数,对一个根是H稳定的k代数,其Nakayama性质在H-cleft扩张下也是不变的.  相似文献   

7.
一类半单Hopf代数的结构   总被引:2,自引:1,他引:1  
董井成 《数学学报》2011,(2):293-300
设k是特征为零的代数闭域,H是k上的pq~2维Frobenius型半单Hopf代数,其中p,q为不同的素数.本文证明了,如果p>q且H~*也是Frobenius型Hopf代数,则H是q~2维群代数A与A上p维Yetter-Drinfeld Hopf代数R的双积,即H≌R#A.作为例子,本文还证明了任意63维或68维的半单Hopf代数均为Frobenius型Hopf代数.  相似文献   

8.
设k是代数闭域,∧是k上基本有限维连通Koszul自入射代数.本文首先证明:如果∧满足有限生成(FG)假设,那么存在∧的k-代数自同构σ0使得关于∧-双模D∧~(σ0)的扭平凡扩张T(∧~(σ0))=∧×D∧~(σ0)亦满足FG假设.由此得到,在∧满足FG假设的条件下,(1)T(A~(σ0))的表示维数大于等于∧的复杂度加2;(2)设G是∧的k-代数自同构群Aut_k(∧)的有限子群,且其阶在∧中可逆.如果对于任意的g∈G都有σ0g=gσ0,那么斜群代数∧*G的扭平凡扩张代数T((∧*G)~(σ0))的表示维数大于等于∧的复杂度加2.  相似文献   

9.
设G是一个有限群,k为一个特征不整除G的阶数的域,∧是一个扭kG-模代数,且∧*σG(简写为∧*G)是一个交叉积代数.设L(R)为代数∧的模范畴中前缀(后缀)的投射(内射)维数至多为1的所有有限生成的不可分解模.本文主要研究了交叉积代数∧*G的模范畴左(右)部分L∧*G(R∧*G)与代数∧的左(右)部分L(R)之间的关系.最后,利用本文得到的结果,考察了代数∧的相关性质在交叉积扩张下在代数∧*G中的保持性.  相似文献   

10.
张光连  王帅 《中国科学A辑》2004,34(2):165-172
Λ是有限域k上的有限维代数, 证明了在molΛ中Green公式成立当且仅当Λ是遗传代数.  相似文献   

11.
We show that all projective resolutions over a monomial relations algebra Λ simplify drastically at the stage of the second syzygy; more precisely, we show that the kernel of any homomorphism between two projective left Λ-modules is isomorphic to a direct sum of principal left ideals generated by paths. As consequences, we obtain:
(a)  a tight approximation of the finitistic dimensions of Λ in terms of the (very accessible) projective dimensions of the principal left ideals generated by paths;
(b)  a basis for comparison of the ‘big’ and ‘little’ finitistic dimensions of Λ, yielding in particular that these two invariants cannot differ by more than 1 and that they are equal in ‘most’ cases;
(c)  manageable algorithms for computation of finitistic dimensions.
This research was partially supported by a grant from the National Science Foundation.  相似文献   

12.
It is shown that the little finitistic dimension of a finite dimensional algebra, i.e., the supremum of the finite projective dimensions attained on finitely generated modules, is not necessarily attained on a cyclic module. In general, arbitrarily high numbers of generators are required. Moreover, it is demonstrated that this phenomenon may depend on the base fieldk. In fact, for each integerd>-3, there exists a quiver Γ with a set ρ of paths such that the little finitistic dimension of the finite dimensional algebrakΓ/<ρ> is attained on a cyclic module precisely when |k|≥d. By contrast, the global dimension of finite dimensional monomial relation algebras does not depend on the base field. This research was partially supported by a grant from the National Science Foundation.  相似文献   

13.
Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another: contravariant finiteness of the subcategory of (finitely generated) left modules with finite projective dimension, finitistic dimension, finite representation type, Auslander algebra, tame or wild representation type. Presented by A. VerschorenMathematics Subjects Classifications (2000) 16L60, 16H05, 16G10.Research supported by the bilateral project BIL99/43 “New computational, geometric and algebraic methods applied to quantum groups and diffferential operators” of the Flemish and Chinese governments.  相似文献   

14.
关于有限维数猜想的一些新进展   总被引:1,自引:1,他引:0  
惠昌常 《数学进展》2007,36(1):13-17
在Artin代数的表示理论中,有一个著名的有限维数猜想:任意给定一个Artin代数,它的有限维数都是有限的.这个猜想已有45年的历史,至今悬而未决.本文主要综述它的一些历史发展情况,并介绍关于有限维数猜想的一些最新进展.  相似文献   

15.
没A是一个有限维代数,R为A的对偶扩张代数.本我们讨论R的有限维数findim R of R,证明了,在—般情况下findim R≠2findim A,这就回答了惠昌常教授所提的一个问题.  相似文献   

16.

Let Λ be an Artin algebra with a unique non-injective indecomposable projective module. In this situation, Marczinzik conjectured that the dominant dimension of Λ agrees with its finitistic dimension. In this paper, we give a proof of a stronger statement. As a byproduct, we obtain excellent control over the finitistic dimensions of Artin algebras with two simples and positive dominant dimension, and also establish the Gorenstein symmetry conjecture for all algebras under consideration.

  相似文献   

17.
Let A be an Artin algebra.We investigate subalgebras of A with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.  相似文献   

18.
Let G be a compact group whose local weight b(G) has uncountable cofinality. Let H be an amenable locally compact group and A(G × H) be the Fourier algebra of G × H. We prove that the group von Neumann algebra VN(G × H) = A(G × H)* has the weak uniform A(G × H)** factorization property of level b(G). As a corollary we show that A(G × H) is strongly Arens irregular, and the topological centre of UC 2(G × H)* is equal to the Fourier–Stieltjes algebra B(G × H).  相似文献   

19.
Given an Ext-injective stratifying system of Λ-modules satisfying that the projective dimension of Y is finite, we prove that the finitistic dimension of the algebra Λ is equal to the finitistic dimension of the category . Moreover, using the theory of stratifying systems we obtain bounds for the finitistic dimension of Λ. In particular, we get the optimal bound 2n-2 for the finitistic dimension of a standardly stratified algebra with n simples.  相似文献   

20.
Let G be a compact p-adic Lie group, with no element of order p, and having a closed normal subgroup H such that G/H is isomorphic to Zp. We prove the existence of a canonical Ore set S* of non-zero divisors in the Iwasawa algebra Λ(G) of G, which seems to be particularly relevant for arithmetic applications. Using localization with respect to S*, we are able to define a characteristic element for every finitely generated Λ(G)-module M which has the property that the quotient of M by its p-primary submodule is finitely generated over the Iwasawa algebra of H. We discuss the evaluation of this characteristic element at Artin representations of G, and its relation to the G-Euler characteristics of the twists of M by such representations. Finally, we illustrate the arithmetic applications of these ideas by formulating a precise version of the main conjecture of Iwasawa theory for an elliptic curve E over Q, without complex multiplication, over the field F generated by the coordinates of all its p-power division points; here p is a prime at least 5 where E has good ordinary reduction, and G is the Galois group of F over Q.  相似文献   

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