查询词典 Lie algebra

The vector has the rich actual background and the widespread application function, it has the algebra and the geometry dual statuses, causes the algebra geometrization, the geometry algebra, has communicated the algebra, the geometry and the trigonometric function, has the good analysis method and the complete structure.

向量具有丰富的实际背景和广泛的应用功能，它具有代数和几何双重身份，使代数几何化、几何代数化，沟通了代数、几何与三角函数，具有良好的分析方法和完整的结构。

Explicitly, they are consist of three classes: If H is semisimple, then H k* for some finite group; If H is not semisimple and the characteristic of k is zero, then H is isomorphic the dual of the cross product between one so called Andruskiewitsch-Schneider algebra and a group algebra; If H is not semisimple and the characteristic of k is not zero, then H is isomorphic the dual of the cross product between one special algebra and a group algebra.

具体地讲，它们共分三类：①如果H是半单的，则H同构与一个群代数的对偶；②如果H是非半单的并且基础域的特征是0的话，则H同构一个所谓Andruskiewitsch-Schneider代数与一个群代数交差积的对偶；③如果H是非半单的并且基础域的特征不是0的话，则H同构于某个特定代数与一个群代数交差积的对偶。

Iseki , this theory contact to be suffused with universal algebra, group theory, ring theory, lattice theory,Boolean algebra,set point topology, toplogical algebra etc. we have already obtained the large quantity result to the research of the BCK algebra.

Iseki引入的代数系统，这一理论联系到泛代数、群论、环论、格论、布尔代数、点集拓扑和拓扑代数等，对BCK代数的研究已经取得了一大批的研究成果。

"Higher Algebra" is a 1978 book "Higher Algebra" in the third edition. 1978 edition was compiled by the authors of their "Higher Algebra Lecture"(1964),"A Concise Course in Advanced Algebra"(1965) based on the changes made of.

高等代数》是1978年出版的《高等代数》的第三版。1978年版则是作者在他们所编的《高等代数讲义》（1964年）、《高等代数简明教程》（1965年）的基础上修改而成的。

Established the qualitative algebra space: proposed the symbol algebra and interval algebra space and applied them to the qualitative reasoning; proposed qualitative logic algebra and applied it to the multi-logic problems.

建立了定性代数空间，提出了符号代数和区间代数空间并分析了在定性推理中的应用；提出了定性逻辑代数空间，并应用于物理量之间的多值逻辑问题。

Secondly, for the spascial AF C* algebra-UHF algebra, I study the linear characterization of 2-local isometry on it: make use of the frame attribute, find the trace state of UHF algebra according to the one of matrix algebra and verify the 2-local isometry is linear.

充分利用UHF代数的结构特点，利用矩阵代数的迹态找到UHF代数的迹态，从而证明了2-局部等距的线性性质。

Some other conditions which the implicative operator of a Implication Algebra should satisfied in a logic system are given. The relations between MV-Algebra and Distributive Implication Algebra, Implication Algebra with condition are gained.

对于偏序集上蕴涵代数中的蕴涵算子引入了一些逻辑条件，得到了偏序集上具有不同条件的蕴涵代数与MV-代数之间的关系，给出了偏序集上蕴涵代数与MV代数之间的几个等价定理。

By utilizing the concepts and methods developed in Algebra Topology,Algebra Geometry and Algebra Representations,we first depicted the concepts and results of Incidence Algebra which reflects the linear structure of underlying posets and Sheaf theory which reflects the topological structure of underlying poset in the framework of Category Theory.

本文综合运用了代数拓扑、代数几何及代数表示论里发展起来的概念与方法，首先在范畴的框架下，对和偏序集的线性结构密切相关的Incidence代数，及与偏序集的拓扑结构紧密联系的层，进行了刻画。

Explicitly, they are consist of three classes: If H is semisimple, then H k* for some finite group; If H is not semisimple and the characteristic of k is zero, then H is isomorphic the dual of the cross product between one so called Andruskiewitsch-Schneider algebra and a group algebra; If H is not semisimple and the characteristic of k is not zero, then H is isomorphic the dual of the cross product between one special algebra and a group algebra.

具体地讲，它们共(来源：5fbfA02BC论文网www.abclunwen.com)分三类：①如果H是半单的，则H同构与一个群代数的对偶；②如果H是非半单的并且基础域的特征是0的话，则H同构一个所谓Andruskiewitsch-Schneider代数与一个群代数交差积的对偶；③如果H是非半单的并且基础域的特征不是0的话，则H同构于某个特定代数与一个群代数交差积的对偶。

In Chapter 2, we will use one-parameter subgroups of the Lie group to develop a version ofNewton\'s method on an arbitrary Lie group for maps from a Lie group to its correspondingLie algebra which is independent of affine connections on the Lie group and differs fromNewton\'s method for sections on Riemannian manifolds.

在第2章中，我们主要研究关于从李群到其李代数的映射f的Newton法的收敛性。利用李群的单参数子群来给出关于映射f的Newton迭代点列，此Newton迭代与李群上的联络无关，也与第1章中研究的Newton迭代不同。

In contrast to the ubiquitous rising-sun-with-rays military flag of the Japanese, Chinese banners and ensigns feature a range of designs.

与遍地都是的太阳军旗不同，中国人的旗帜和徽章设计得各式各样。

From their small corner of Feng's Guangzhou headquarters -- a jumble of pink leashes, squeezable rubber steaks, and plastic doggy Santas for Fido's stocking -- Soleil's designers come up with at least five new products a month.

从Feng 设在广州总部的产品展示柜台上可以看到，Soleil的设计师每月至少设计出5件新产品。