代数

The weyl algebras are important because some classical Lie algebras are equivalent to that of the Weyl type algebras.

因为李超代数在物理学中有着重要的作用，并且李超代数紧密的依赖于李代数。

Schauengurg[2] considered more general case and found necessary and sufficient conditions for the cosmash product coalgebra H Q to be a Hopf algebra with a Hopf subalgebra H and a weak projection !

Schauenburg在文献[2]中把Radford的研究加以推广，给出了使余smash积HQ为Hopf代数，H为HQ的子Hopf代数，且具有弱投射π：HQ→H(即π是左模余代数同态，且π|_H=id_H)的等价条件。

We study the definition of bialgebra and prove the sufficient conditions about a bialgebra is commutative and cocommutative.

从双代数的定义入手，给出了双代数成为交换和余交换双代数的两个充分条件。

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。

Finite commutative group; Symmetric bicharacter; Lie color superalgebra ; Left color symmetric algebra ; Left color symmetric structure

基础科学，数学，代数、数论、组合理论有限交换群；对称双特征标；着色李超代数；左着色对称代数；左着色对称结构

Put forward a commutative law in the weak fuzzy implication algebra;The properties of weak FI-algebra and FI-algebra are studied.

引入可交换弱FI代数的概念，讨论了弱FI代数和FI代数的几个性质；进一步得到了交换弱FI代数和交换FI代数的一些结果。

Ringrose began to study nest algebras in the 1960s, many people have devoted themselves to the study of non-selfadjoint and reflexive operator algebras including nest algebras, commutative subspace lattice algebras, completely distributive subspace lattice algebras and so on, and obtain a lot of beautiful achievements.

自从60年代J.Ringrose开始研究套代数以来，人们对套代数、交换子空间格代数和完全分配子空间格代数等非自伴自反算子代数进行了深入研究，并且取得了大量出色的研究成果。

Further some equivalent conditions for a trivial algebra are given, and that the mapping which maps the subset of the universal to the maximal congruence that saturates the subset being a -homomorphism, being order preserving, being constant mapping, the algebra being trivial are equivalent is proved.

最后利用该同余给出了关于平凡代数的几个等价条件，证明了泛代数的子集到渗透该集的最大同余的映射为保序映射、该映射为-同态、该泛代数平凡等是等价的。

Furthermore, we define a convolution multiplication between characteristic functions of constructible subsets by using push-forward functor from the category of algebraic varieties over C to the category of spaces of constructible functions. We construct geometric model for "intrinsic symmetry" of the octahedral axiom in a triangulated category. Using it, we deduce the multiplication satisfies the Jacobi identity of Lie algebra and then realize infinite dimensional Lie algebras.

进一步，我们使用复代数簇范畴到可构函数空间范畴的pushforward函子，给出了可构集上特征函数的卷积乘法，并构造了三角范畴八面体公理的内蕴对称性的几何模型，最终证明了对于不可分解支撑有界可构集的特征函数，乘法满足李代数定义的Jacobi恒等式，从而给出了无限维李代数的实现。

This paper mainly study the relations between some algebraic properties of Roe algebras and the coarse geometry of metric spaces, and its applications to the reduced crossed product C-algebras and the coarse Baum-Connes conjecture.

本文主要研究这类C~*-代数的某些性质与底空间几何之间的联系及其在交叉积C~*-代数和粗Baum-Connes猜测中的应用。第一章研究交叉积C~*-代数的Schwartz型谱不变子代数。

I will endeavour to find you some assistance.

我尽力帮你找人帮忙。

At first I only know bruck is the idol of American younglings, afterwards I returned back to Taiwan ,even in Beijing last year ,I saw her poster everywhere, I was so surprised at her charm.

起初我只晓得布鲁克雷德丝是美国少男少女崇拜的偶像，后来回台湾，甚至去年在北京，居然也四处看见她的海报，才惊讶她的魅力之大。