H~＊－有理模和右Smash积A＃~R_HH~＊ 

本文对Ｈ￣＊上的有理模Ｍ做了一些讨论，刻划了此类模的某些性质，并利用这些性质得到了右Ｓｍａｓｈ积Ａ＃［ｋＧ］上模Ｍ是完全可约模的条件。     

Smash积,辫积和L-R Smash积的新对偶

本文主要地证明:由H-重模代数A,B构成的Smash积A#B的新对偶H(A#B)~0恰好是由重模余代数_HA~0,_HB~0构成的Smash余积_HA~0×_HB~0;如果(H,σ)是辫化Hopf代数,则新对偶_HH~0是右,左H~0-重模余代数;由量子Yang-Baxter H-模代数A,B构成的辫积AαB的新对偶(AαB)~0恰好是由量子Yang-Baxiter H-模余代数_HA~0,_HB~0构成的辫余积_HA~0×_HB~0.最后它给出由H-双模代数A构成的L-R Smash积A■H的新对偶(A■H)_H~0的正合序列。     

分次环，A，Aｅ和Smash积A＃G*是亚直既约环的条件

讨论了分次环Ａ，Ａ_ｅ和Ａ＃Ｇ^*的相关性质，在Ａ是分次忠实时，Ａ＃Ｇ^*是亚直既约环当且仅当Ａ_ｅ是亚直既约环；在Ａ是分次非退化时，Ａ＃Ｇ^*是Ｇ亚直既约环当且仅当Ａ是分次亚直既约环．     

Hilbert C*模及其有界模映射

设E为C^*代数A上可数生成的Hilbert模,B(E)为E上有界模映射全体,则B(E)保距同构于K(E)的左乘子,其中K(E)为E上“紧”模映射全体。当A为无限维本原C^*代数且E为自对偶模,则E为代数有限生成。     

Smash积代数和量子模范畴中的Hopf代数的新对偶

本文引入模代数的一种新对偶,它推广了代数的有限对偶概念.并证明通过这种新对偶,模代数的对偶为余模余代数,从而形成Smash余积,而且证明了Smash积的对偶是Smash余积,即有(A#H)0≌HA0×H0余代数同构.最后证明量子模范畴中的Hopf代数通过这种新对偶是自对偶的.     

Smash积代数和量子模范畴中的Hopf代数的新对偶

本文引入模代数的一种新对偶,它推广了代数的有限对偶概念,并证明:通过这种新对偶,模代数的对偶为余模余代数,从而形成Smash余积,而且证明了Smash积的对偶是Smash余积,即有(A#H)~0 _HA~0×H~0余代数同构,最后证明量子模范畴中的Hopf代数通过这种新对偶是自对偶的。     

分次环的Smash积A#G*与单位分量Ae理想间的对应

本文对任意群G上的任意分次环A,建立了Smash积A#G^*和单位分量A_e理想间的对应关系,并运用所建立的对应关系研究分次环的Smash积A#G^*和A_e的半素性,素性和单性.     

弱Hopf代数的对偶定理及Smash积的模结构

本文主要包括两方面内容:首先将Hopf代数理论中的对偶定理部分地推广到弱Hopf代数的情况;然后讨论弱Hopf代数上的Smash积的模及模同态,并部分地推广了Maschke-type定理．     

Hilbert C*模上的Gabor酉系统

本文引入了Hilbert C*-模上的Gabor酉系统的概念,研究了它的基本性质,证明了膨胀定理,并给出某个酉系统的两个正规框架向量不相交的等价条件.     

一个与G－分次环和G－集的Smash积有关的Maschke－Type定理

对任意群Ｇ，［１］研究了有单位元１的Ｇ－分次环与有限可迁Ｇ－集的Ｓｍａｓｈ积．在本文中，我们对任意可迁Ｇ－集Ａ讨论了具有局部单位元的Ｇ－分次环与Ｇ－集Ａ的Ｓｍａｓｈ积，证明了有关的一个Ｍａｓｃｈｋｅ－ｔｙＰｅ定理．推广了［２］［３］中的一些重要结果．     

Commuting Homotopy Limits and Smash Products

In general the processes of taking a homotopy inverse limit of a diagram of spectra and smashing spectra with a fixed space do not commute. In this paper we investigate under what additional assumptions these two processes do commute. In fact we deal with an equivariant generalization that involves spectra and smash products over the orbit category of a discrete group. Such a situation naturally occurs if one studies the equivariant homology theory associated to topological cyclic homology. The main theorem of this paper will play a role in the generalization of the results obtained by Bökstedt, Hsiang and Madsen about the algebraic K-theory Novikov Conjecture to the assembly map for the family of virtually cyclic subgroups.     

Reduced Crossed Products of Pro-Banach Algebras*

This paper gives the concept of the reduced pro-Banach algebra crossed product associated with inversely pro-Banach algebra dynamical system, and shows that the reduced crossed product is an inverse limit of an inverse system of Banach algebra crossed products. Also, the authors show that if the locally compact group is amenable, then the crossed product and the reduced crossed product are isometrically isomorphic.     

双边弱smash积的Maschke型定理

本文主要给出半单弱Hopf代数上双边弱Smash积的Maschke型定理.     

On Smash Products Of Hopf Algebras

Let H = X? _R A denote an R-smash product of the two bialgebras X and A. We prove that (X,A) is a pair of matched bialgebras, if the R-smash product H has a braiding structure. When X is an associative algebra and A is a Hopf algebra, we investigate the global dimension and the weak dimension of the smash product H = X? _R A and show that lD(H) ≤ rD(A) + lD(X) and wD(H) ≤ wD(A) + wD(X). As an application, we get lD(H ₄) = ∞ for Sweedler's four dimensional Hopf algebra H ₄. We also study the associativity of smash products and the relations between smash products and factorization for algebras.     

分次Morita对偶，Morita对偶与Smash积

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。     

Free Subproducts and Free Scaled Products of II1-Factors

The constructions of free subproducts of von Neumann algebras and free scaled products are introduced, and results about them are proved, including rescaling results and results about free trade in free scaled products.     

Twisted Smash Products and L-R Smash Products for Biquasimodule Hopf Quasigroups

We consider two new algebras from an H-biquasimodule algebra A and a Hopf quasigroup H: twisted smash product A ? H and L-R smash product A?H, and find necessary and sufficient conditions for making them Hopf quasigroups. We generalize the main results in Brzeziński and Jiao [5] and Klim and Majid [9]. Moreover, if H is a cocommutative Hopf quasigroup, we prove that A ? H is isomorphic to A?H as Hopf quasigroups.     

Hopf代数的冲积的弱整体维数

设H是有限维Hopf代数,A是交换的H-模代数。当H~*是幺模且A中存在迹为1的元素时,本文证明冲积A#H与代数A的弱整体维数相等。