上同调

基本解释 (translations)

cohomology

与上同调相关的网络例句 [注：此内容来源于网络，仅供参考]

After that, using the method of group action we get the formula for computing of dimensions of cohomology of holomorphic vector bundles with trivial pull-back on non-primary Hopf manifold, of which the fundamental group is Abelian 〓.

我们利用群作用的方法，给出了具有Abel基本群〓的非主Hopf流形上具有平凡拉回的全纯向量丛的上同调维数的计算公式。

Let L and P be Lie color algebras and let M be a graded module over P, the crossed modules which make M as their kernal and P as their cokernal are considered. It is shown that under a suitable equivalent relation, there is a bijection between the set of the equivalent classes CML and the homogeneous components of degree zero of H~3.

从交叉模的定义出发，对于给定的Lie color代数L，P以及阶化P模M，考虑所有以M为核、以P为余核的L的交叉模，在这些交叉模之间定义了一个等价关系，由此得到交叉模的等价类集CML，证明了CML与三维上同调群H~3的零次齐次部分之间存在一一对应，从而可以利用三维上同调群对Lie color代数的交叉模进行分类。

It proves that the first cohomology group of Block Lie algebraL with coefficients inL-module V is trivial.

证明了系数在模V上的Block型李代数的一阶上同调群是平凡的。

The theory of homology and cohomology is very important in mathematics.

同调与上同调理论在数学中占有很重要的地位。

The main purpose of this thesis is to study the application of the representation theory in Hochschild homology and cohomology groups of algebras, Hopf algebras and quantum groups, which are very active branches at present.

本学位论文主要研究代数表示论在代数的Hochschild同调群和上同调群，Hopf代数和量子群这几个当今很活跃的数学分支中的应用。

In the representation theory of finite-dimensional algebras, combinatorial tools as quivers and their representations provide effective method in computing Hochschild homology and cohomology groups of finite-dimensional algebras.

代数表示论中的组合工具—箭图及其表示的发展和应用，为计算有限维代数的Hochschild同调群与上同调群提供了有效的方法。

In particular, we compute Hochschild homology and cohomology groups of infinitedimensional path algebras and some of their quotient algebras, and we prove that for a general monomial algebra (not necessary finite-dimensional), all Hochschild cohomology groups of positive degrees vanish if and only if its Gabriel quiver is a finite tree.

特别地，我们计算了无限维路代数以及某些商代数的Hochschild同调群和上同调群，而且给出了一般单项代数的各正次Hochschild上同调群为零的充分必要条件，即它的Gabriel箭图是有限树。

We've found that on symplectic manifolds there exists a series of Euler-Lagrange cohomology groups different from both de Rham and harmonic cohomology in general and proposed a set of general volume-preserving equations that contain the Hamiltonian equations as a special case.

中文摘要：我们发现在作为经典力学中的相空间的辛流形上有可能存在不同于de Rham上同调和调和形式的上同调，称之为Euler-Lagrange上同调；提出相空间上保体积的一般方程，通常的正则方程是其特殊形式；进而推广了经典力学中著名的刘维定理；同时把Noether定理与上同调联系起来。

The contents include the computing of dimensions of cohomology of line bundles on non-primary Hopf manifolds and their applications to the existence problem of holomorphic structure or filtrable holomorphic structure on a continuous vector bundles; the structure and the computing of dimensions of cohomology of holomorphic vector bundles with trivial pull-back.

在这篇博士学位论文中，我们研究了非主Hopf流形上全纯向量丛，主要包括：非主Hopf流形上全纯线丛的上同调维数的计算，以及它们对连续向量丛上全纯。。。

In chapter 2, we study a kind of operator algebra acted on the Hilbert space H which is called the closed weakly reducible maximal triangular algebra, denoted by S.

第二章我们研究了一个作用在Hilbert空间Η上的闭弱可约极大三角代数S，证明了S的系数在Β中的任意阶完全有界Hochschild上同调群H_~nS，Β(Η(n≥1)是平凡的。

与上同调相关的网络解释 [注：此内容来源于网络，仅供参考]

cohomology coboundary homomorphism：上同调上边缘同态

cohomology class | 上同调类 | cohomology coboundary homomorphism | 上同调上边缘同态 | cohomology exact sequence | 上同调正合序列

cohomological dimension：上同调维数

cohobation | 回流蒸馏 | cohomological dimension | 上同调维数 | cohomology algebra | 上同调代数

cohomology algebra：上同调代数

cohomological dimension | 上同调维数 | cohomology algebra | 上同调代数 | cohomology class | 上同调类

cohomology module：上同调模

上同调类|cohomology class; cohomology class | 上同调模|cohomology module | 上同调平凡模|cohomologically trivial module

cohomology operation：上同调运算

上同调群|cohomology group; cohomology group | 上同调运算|cohomology operation | 上同伦群|cohomotopy group

cohomology ring：上同调环

上同调|cohomology; cohomology | 上同调环|cohomology ring | 上同调类|cohomology class; cohomology class

cohomology spectral sequence：上同调谱序列

上同调平凡模|cohomologically trivial module | 上同调谱序列|cohomology spectral sequence | 上同调群|cohomology group; cohomology group

cohomology exact sequence：上同调正合序列

cohomology coboundary homomorphism | 上同调上边缘同态 | cohomology exact sequence | 上同调正合序列 | cohomology of a coproduct | 上积的上同 调

cohomology theory：上同调论

cohomology ring | 上同调环 | cohomology theory | 上同调论 | cohomology | 上同调

cohomology of semisimplicial complex：半单纯复形的上同调

cohomology of a group | 群的上同调 | cohomology of semisimplicial complex | 半单纯复形的上同调 | cohomology operators | 上同调算子