交叉积的同调维数

本文证明了当H是有限维半单和余半单的Hopf代数时,R与交叉积R#σH的整体维数是相同的;同时,它们的弱维数也是相同的.     

交叉积的同调维数

本文证明了当Ｈ是有限维半单和余半单的Ｈｏｐｆ代数时,Ｒ与交叉积Ｒ＃σＨ的整体维数是相同的;同时,它们的弱维数也是相同的．     

关于对偶扩张代数有限维数的注记

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．     

von Neumann代数交叉积的注记

设A是B(H)中的极大交换*-子代数, G是离散群,在不要求G自由地作用在A的情况下,得到了交叉积A×αG是因子的充分且必要条件.     

弱群余代数的交叉积

该文引入弱群交叉积的概念,并给出弱群交叉积代数和通常的张量积余代数构成弱半Hopf群余代数的充要条件,接着证明了弱群交叉积上的对偶定理,推广了沈和王~([7-8])的主要结果.     

冯·诺依曼代数交叉积的一点注记

设α是可数离散群G和H的半直积G■_σH在冯·诺依曼代数M上的作用,则β_h=α_((e,h))AdU_h定义了群H在冯·诺依曼代数交叉积M■_αG上的作用β.本文证明了交叉积冯·诺依曼代数M■_α(G■_σH)与(M■_αG)■_βH是*-同构的,因此在一定条件下,冯·诺依曼代数的交叉积满足结合律.     

投射模的自同态代数与有限维猜想北大核心CSCD

设代数A是整体维数有限的Artin代数,e是A的一个幂等元,则e Ae的有限维数有限,如果以下条件满足其一:(a)rep.dim(A/Ae A)≤3,且对任意单A/Ae A-模K,有proj.dim(AK)≤4;(b)对任意单A/Ae A-模K,都有proj.dim(AK)≤3.     

Hopf代数交叉积的同调维数

Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra, ln this paper, we characterize the projectivity (injectivity) of M as a left A#σ H-module when it is projective (injective) as a left A-module. The sufficient and necessary condition for A#σ H, the crossed product, to have finite global homological dimension is given, in terms of the global homological dimension of A and the surjectivity of trace maps, provided that H is cocommutative and A is commutative.     

$A_n-$型有限维代数的整体维数

设$k$是一个代数闭域, $n$是一个自然数,本文给出了一个精确刻画$A_{n}$-型有限维$k$-代数的整体维数的技巧.据此给出了$A_{n}$-型有限维$k$-代数的所有可能的整体维数.特别的,如果$n>1$,我们指出其中最大的是 $n-1$,最小的是 $1$.     

斜群代数与平凡扩张的表示维数

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.     

A Note on Finitistic Dimension of Hopf-Galois Extensions

Let H be a finite-dimensional Hopf algebra over a field k and A/B be a right H-Galois extension. If the functors A ?_B ? and _B(?) are both separable, then the finitistic dimension of A is equal to that of B.     

Cat1-Hopf Algebras and Crossed Modules

A reductive monoid M is called 𝒥-irreducible if M?{0} has exactly one minimal G × G-orbit. There is a canonical cellular decomposition for such monoids. These cells are defined in terms of idempotents, B × B-orbits, and other natural monoid notions. But they can also be obtained by the method of one-parameter subgroups. This decomposition leads to a number of important combinatorial and topologial properties of the monoid of B × B-orbits of M. In case M?{0} is rationally smooth these cells are closely related to affine spaces. They can be used to calculate the Betti numbers of a certain projective variety.     

Primes of Gauss Extensions Over Crossed Product Algebras

Let K be a skew field with total subring V and G be a right ordered group with cone P, so that the crossed product algebra K*G has a skew field D of fractions. We consider total subrings R of D with R ∩ K = V, describe the overrings in D, as well as subrings of R. For particular extensions R of V we determine the prime ideals of R in terms of prime ideals of V and prime ideals of overcones of P in G.     

Crossed Products for Weak Hopf Algebras

Weak crossed products by a weak bialgebra are defined. The resulting structure is not that of a unital algebra but an associative algebra with preunit. A general formula of such a product is given in terms of a weak 2-cocycle and a weak measuring. The relation with weak cleft extensions is studied. Equivalences of weak crossed products are defined and are related to gauge transformations. A relation between cleaving maps is described in terms of gauge transformations.     

Equivalent Crossed Products and Cross Product Bialgebras

In a previous article we proved a result of the type “invariance under twisting” for Brzeziński's crossed products. In this article we prove a converse of this result, obtaining thus a characterization of what we call equivalent crossed products. As an application, we characterize cross product bialgebras (in the sense of Bespalov and Drabant) that are equivalent (in a certain sense) to a given cross product bialgebra in which one of the factors is a bialgebra and whose coalgebra structure is a tensor product coalgebra.     

Crossed products on the flow of groupoid with quasi-invariant measures

LetG be a second countable groupoid with Haar system {λ ^u },A be an abelian group which left invariant acts onG. Then we have aC ^*-dynamic system (C ^* (G, A, β). In this paper we have studied the existence of quasi-invariant measure with certain properties; using these measures some important results about crossed products and groupoidC ^*-algebras have been obtained. This work is supported by National Natural Science Foundation of China