可解二次Lie代数

一个带有非退化、对称不变双线性型的Lie代数称为二次Lie代数. 研究可解二次Lie代数的结构, 特别是Cartan子代数由半单元构成的可解二次Lie代数. 从上同调的观点出发给出了一种构造二次Lie代数的方法, 并证明了可解二次Lie代数均可用此方法构造.     

Cohomology Complex Projective Space with Actions of G_5

§1. Introduction A cohomology complex projective nspace is a smooth, closed, orientable 2nmanifold M2n such that there is a class x∈H2(M; Z) with the property that H*(M; Z)=z［x］/(xn+1). Let i: K2n-1M2n be the inclusion map of a closed, connected, orientable submanifold and d is an integer; we say that the degree of K2n-2 is d, if i*［K］ is the Poincaré dual of dx. We always assume that the orientation of K2n-2 is chosen in such a way that d is nonnegative. Let p be a prime number…     

李color三系的上同调和Nijenhuis算子

本文研究了李color三系的上同调结构和Nijenhuis算子的问题.利用李三系的上同调和Nijenhuis算子的研究方法,构造出李color三系的上边界算子,获得了李color三系的单参数形式形变.推广了线性映射生成无穷小形变的充分必要条件,同时证明了由一个李color三系的Nijenhuis算子产生的形变是平凡的.     

拟entwining结构的Hochschild上同调

本文给出了拟entwining结构的概念,研究了拟entwining结构的Hochschild上同调,得到了关于拟entwining结构的Hochschild上同调的等价定理.特别地,对于有限维代数和余代数的拟entwining结构,给出了余代数结构的Hochschild上同调与对偶代数结构的Hochschild上同调之间的同构定理.     

Curvature, Diameter and Bounded Betti Numbers

In this paper, we introduce the notion of bounded Betti numbers, and show that the bounded Betti numbers of a closed Riemannian n-manifold (M, g) with Ric (M) ≥ -(n - 1) and Diam (M) ≤ D are bounded by a number depending on D and n. We also show that there are only finitely many isometric isomorphism types of bounded cohomology groups (H*(M), || · ||∞) among closed Riemannian manifold (M, g) with K(M) ≥-1 and Diam (M) ≤ D.     

交换Hopf代数扭余作用下的余代数的上同调

该文证明了若交换Hopf代数在余代数C上的扭余作用的coassociator是卷积可逆的,那么该扭余作用也是可逆的.在这种情形下,给出了余代数C的正则上同调的定义,并且证得每个可逆的扭余作用可以提升到H的系数属于C的一个三次正则上同调类,且扭余作用的obstruction是平凡的当且仅当该扭余作用对应着一个cleft余扩张.     

拓扑量子场理论与相交指标

该文构造了一新的上同调型拓扑量子场理论并证明了其配分函数是相交指标 (crossingindex)     

自守形式Eichler上同调的Knopp猜想

部分地证明了Knopp关于H 群上自守形式的Eichler上同调的一个猜想 .     

局部上同调模的Artin性质

In this paper,let (R,m)be a Noetherian local ring,I(?)R an ideal, M and N be two finitely generated modules.Firstly,we study the properties of H_I~t(M),t=f-depth(I,M) and discuss the relationship between the Artinianness of H_I~i(M,N) and the Artinianness of H_I~i(N).Then,we get that H_I~d(M,N)is I-cofinite,if(R,m)is a d-dimensional Gorenstein local ring.     

具孤立奇点的完全交叉的上同调(三)

本文证明了不可约超曲面孤立奇点的无穷小邻域的全微分形式的上同调是有限维线性空间,并证明了它们与通常微分形式上同调之间的关系.