查询词典 algebras

In this paper, we develop the theory of Killing form over any finite dimensional Hopf algebras, and discuss the deep relations between the non-degeneracy of Killing form and the adjoint representations of Hopf algebras.

中文摘要：本硕士论文的主要内容是在有限维Hopf代数上建立了Killing型的一般理论，揭示了Killing型的非退化性与Hopf代数的伴随表示之间的深刻联系。

Then in [2], [3], [4] and [5], the authors have discussed the structures of twisted Hopf algebras and bitwisted Hopf algebras and studied some properties of their antipodes, and so on.

在文献[2]、[3]、[4]和[5]中，作者分别研究了扭Hopf代数和双扭Hopf代数的结构和反极元的性质等。

Then we deeply studied the completeness of LP . Consequently, we established:(1) The completeness theorem of LP with truth-value in finite Lukasiewiczchain;(2) The completeness theorem of LP with truth-value in complete and atomic lattice implication algebras;(3) The completeness theorem of LP with truth-value in injective lattice implication algebras.

建立了：（1）基于Lukasiewicz有限链的格值命题逻辑系统LP的完备性定理；（2）基于完备的且原子的格蕴涵代数的格值命题逻辑系统LP的完备性定理；（3）基于内射的格蕴涵代数的格值命题逻辑系统LP的完备性定理。

The theory of the representations of Virasoro algebras is well developed,however,the representation theory of Caftan type Lie algebras is far from being well developed.

当参数趋向于1时，李代数的量子形变就回到原来的李代数；另外，李代数的一些性质在它的量子形变中仍然保持。

The course contains four sections as follows: mathematical logic (including basic concepts of propositional logic and predicate logic, propositional calculuses and inference theories), set theory (including set algebras, relations, functions and cardinal numbers), algebraic structure (including algebraic systems, semigroups and groups, rings and fields, lattices and Boolean algebras), graph theory (including basic concepts of graph, Euler graphs and Hamiltonian graphs, trees, planar graphs and coloring graphs, some special vertex subsets and edge subsets).

本课程包含四部分内容：数理逻辑（包含命题逻辑与一阶逻辑的基本概念、等值演算以及推理理论），集合论（包含集合代数、二元关系、函数和基数），代数结构（包含代数系统、半群与群、环与域、格与布尔代数），图论（包含图的基本概念、欧拉图与哈密顿图、树、平面图及图的着色、图的某些特殊的顶点子集与边子集）。

The relation allows us to evaluate coupling and re_coupling coefficients of the corresponding quantum and classical Lie algebras from the induction and subduction coefficients of their centralizer algebras.

这一关系使我们能够利用相应中心代数的诱导及分导系数计算出经典李代数及其量子情形的耦合与重新耦合系数。

Many of important concepts in the theory of abstract Lie algebras come from classical theory of groups, for example, complete Lie algebras is a generalization of complete groups.

李代数的抽象理论中很多重要的概念都来源于经典群论，完备李代数便是一个例子。

We give some examples of BiFrobenius algebras based on the extensions of algebras and coalgebras . Let H be a bialgebra of finite dimension . Then T= H⊕H* has an algebra structure and a coalgebra structure also . We discuss the properties of T , and get the necessary and sufficient condition for T to be a BiFrobenius algebra .

然后根据代数余代数的平凡扩张给出一类BiFrobenius代数的例子，设H是有限维双代数， T= H⊕H*既有代数结构也有余代数结构，研究T的性质，给出了T成为BiFrobenius代数的充要条件，即定理3.9。

Ringel has given and studied the N_0I-graded twisted coalgebra and Ringel-Hall algebra in the reference [1]. Subsequently, people found that there is an analogy between Ringel-Hall algebra and Hopf algebra, and then they introduced the concept of twisted Hopf algebras and bitwisted Hopf algebras, and worked on them.

Ringel在[1]中引入并研究了N_0I-分次扭的余代数和Ringel-Hall代数，后来人们发现Ringel-Hall代数有类似Hopf代数的结构，随后，扭Hopf代数、双扭Hopf代数先后被引入和研究。

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。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。