Yetter–Drinfeld Modules over the Hopf–Ore Extension of the Group Algebra of Dihedral Group

Let k be an algebraically closed field of characteristic zero, and D _n be the dihedral group of order 2n, where n is a positive even integer. In this paper, we investigate Yetter-Drinfeld modules over the Hopf-Ore extension A(n, 0) of kD _n . We describe the structures and properties of simple Yetter-Drinfeld modules over A(n, 0), and classify all simple Yetter-Drinfeld modules over A(n, 0).     

Cosemisimple Coextensions and Homological Dimension of Smash Coproducts

Let H be a finite dimensional cosemisimple Hopf algebra, C a left H-comodule coalgebra and let C = C/C（H^＊）^＋ be the quotient coalgebra and the smash coproduct of C and H. It is shown that if C/C is a eosemisimple coextension and C is an injective right C-comodule, then gl. dim（the smash coproduct of C and H） = gl. dim（C） = gl. dim（C）, where gl. dim（C） denotes the global dimension of coalgebra C.     

具有三角分解李代数的积分元和中心扩张

本文将应用广义限制李代数的概念来研究具有三角分解李代数的积分元和中心扩张的关系.对于给定的广义限制普遍包络代数,我们确定了它的积分元并且提供了一种计算dim H2(L,F)的方法.     

区间上单峰扩张自映射周期轨道的超旋转对

设f是区间I=[0,1]上的单峰扩张自映射, k ∈N,m≥2,λm,k是方程x(k-1)m(xm- 1)Q(x,m 1) (x(k-1)m-1)Q(x,m)=0在(1, ∞)上的唯一实根,其中Q(x,m)=(xm- 2xm-1 1).本文证明:若f的扩张常数λ≥λm,k,则f有超旋转对为(k,km 1)的周期轨道. 此外,还指出,当1<λ<λm,k时,在区间上存在单峰扩张自映射具有扩张常数λ却无超旋转对为(k,km 1)的周期轨道.     

纯无限单C*-代数的扩张代数的K-理论Ⅱ

给出了有单位元的纯无限单的C*-代数A通过K的扩张代数E的K-理论的一种刻画.证明了K0(E)同构于E中所有具有无限余投影的无限投影的Murry-yon Neumann等价类全体所成的交换群,它还同构于上述投影的同伦等价类或酉等价类全体所成的交换群.还证明了对扩张代数E中的任·满的正元a,存在元索z ∈E,使得x*ax=1,其中K为可分无限维Hilbert空间上紧算子全体所成的C*一代数.     

Mann iteration of weak convergence theorems in Banach space

In this paper, by using Mann＇s iteration process we will establish several weak convergence theorems for approximating a fixed point of k-strictly pseudocontractive mappings with respect to p in p-uniformly convex Banach spaces. Our results answer partially the open question proposed by Marino and Xu, and extend Reich＇s theorem from nonexpansive mappings to k-strict pseudocontractive mappings.     

一类Block型李代数的分类和中心扩张

本文我们决定了一类Block型李代数$\BB$在同构意义下的分类和中心扩张, 其中$q$是一个非零复数. 我们的结果推广了以前的一些结果.     

具有对称自同态的环

通过引入对称α-环的概念,拓广对称环的研究.讨论对称α-环与相关环的关系,给出对称α-环的一些扩张性质,证明了1)设α是约化环R的自同态且α-1)=1.如果R是对称α-环,则R[x]/〈x~n〉是对称α-环;2)设α是右Ore环R的自同构,Q(R)是R的典范右商环.如果R是对称环,则R是对称α-环当且仅当Q(R)是对称α-环.     

Augmented Spinor Space

In this paper, based on the Pauli matrices, a notion of augmented spinor space is introduced, and a uniqueness of such augmented spinor space of rank n is proved. It may be expected that this new notion of spaces can be used in mathematical physics and geometry.     

弱Hopf代数上的Militaru-Stefan提升定理

本文研究了弱Hopf-Galois扩张的扩张模.利用忠实平坦的弱Hopf-Galois扩张理论,研究了弱Hopf代数上的Militaru-Stefan提升定理,推广了文献[10]中的相应结果.进一步地,通过诱导模的自同态环的cleft扩张刻画了弱稳定模.