Hopf Superquivers

In this paper, a super version of the Hopf quiver theory is developed. The notion of Hopf superquivers is introduced. It is shown that only the path supercoalgebras of Hopf superquivers admit graded Hopf superalgebra structures. A complete classification of such graded Hopf superalgebras is given. A superquiver setting for general pointed Hopf superalgebras is also built up. In particular, a super version of the Gabriel type theorem and the Cartier-Gabriel decomposition theorem is given.     

DARBOUX TRANSFORMATION OF A NONLINEAR EVOLUTION EQUATION AND ITS EXPLICIT SOLUTIONS

In this paper, we study a differential-difference equation associated with discrete 3 × 3 matrix spectral problem. Based on gauge transformation of the spectral problm, Darboux transformation of the differential-difference equation is given. In order to solve the differential-difference equation, a systematic algebraic algorithm is given. As an application, explicit soliton solutions of the differential-difference equation are given.     

Morita context of weak Hopf algebras

Let H be a finite-dimensional weak Hopf algebra and A a left H-module algebra with its invariant subalgebra A~H.We prove that the smash product A#H is an A-ring with a grouplike character, and give a criterion for A#H to be Frobenius over A. Using the theory of A-rings, we mainly construct a Morita context connecting the smash product A#H and the invariant subalgebra A~H , which generalizes the corresponding results obtained by Cohen, Fischman and Montgomery.     

On the braided structures of Radford's biproduct

We obtain the necessary and sufficient conditions for Radford’s biproduct to be a braided Hopf algebra. As an application, a nontrivial example is given.     

群在von Neumann代数上作用的自由和遍历性注记

本文研究了群在von Neumann代数上作用的自由性和遍历性问题.利用投影和群SL2(R)的Iwasawa分解,得到了可数离散群在交换von Neumann代数上作用的自由性的等价刻画,证明了SL2(R)在上半平面H上有理作用导出的SL2(R)在极大交换von Neumann代数A={Mf:f∈L2(H,dxdy/y2)}上的作用α是遍历的,但不是自由的.     

三角代数上初等映射的可加性

本文主要研究了三角代数上的初等映射的可加性.利用矩阵分块理论,证明了三角代数上的初等映射是可加的.     

泛欧氏空间的Clifford群、扭群、旋群及它们的李代数

本文研究了泛欧氏空间的Clifford群、扭群、旋群,它们为Clifford代数中选出极好的一类子群.利用Clifford代数理论方法,获得了泛欧氏空间中Clifford群、扭群、旋群及其李代数的结构及它们之间的关系,并且得到了它们的李代数.     

单项代数的一个注记

本文研究单项代数上模的同调性质.应用Huisgen-Zimmermann的著名结果,分别给出了由一条道路生存的投射模及好模存在的充分条件.     

一道学情调研题的解题建议

解析几何综合题的运算量大,恐怕是同学们解题的共识.那么,如何根据问题的条件寻找与设计合理、简捷的运算途径,进而简化解析几何综合题的运算量呢?这里借助一道学情调研题,给同学们提点解题建议.题目(江苏省南京市2011届高三学情调研卷第19题)已知圆M的圆心M在y轴上,半径为     

球面上两点间距离的微分学证明

在高中数学选修课程《球面上的几何》中,球面上两点间距离的概念依赖如下结论:结论1设A,B是球面上两点,在连接A,B两点的球面曲线段中,以过这两点的大圆弧中的劣弧长最短.教材对结论1作了一个直观解释,却并未给出严格证明,本文将用微分学知识对这个结论作一论证.引理1三面角中任意两个面角的和大于第三