查询词典 killing form

We know that a Killing form is a trace form under adjoint represen-tation.

所谓killing型是指关于伴随表示的迹型。

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。

We develop his ideas by finding some algebraic invariants under the adjoint actions of the group in addition to the Killing form and give a rigorous proof of the optimality of the one-parameter systems for the symmetry group of the given equations.

本文系统地研究了1+2维非线性发展方程的对称代数，证明了该方程容许一个七维李点对称群，利用Olver提出的方法，详细地建构了1+2维非线性发展方程的一维最优系统，在此基础上我们发展了他的方法，发现了除Killing型之外的其它六个在群伴随作用下的代数不变量，利用这些不变量证明了该最优系统的最优性。

All real simple Malcev algebra,are classified according to whether or not they have a compatible complex structure and simultaneously we give all the invariant bilinear forms by the killing form of the real simple Malcev algebra or the killing form of it s complexification .

研究实单Malcev代数上的不变双线性型，仿照李代数的情形给出实Malcev代数上的容许复结构、实Malcev代数的复化以及Malcev代数上的不变双线性型等概念，并通过对实单Malcev代数上容许复结构的讨论，将实单Malcev代数上的不变双线性型分为两种情形。

Then we study the typical property of theirs form the starting of nature and constitute of the two types of Lie algebra, and we calculated separately their dimension, center, commutator algebra, Killing type, Cartan subalgebra, structure formula, root system, and so on.

本文主要研究了两类典型的李代数即李代数so*(2n)和g*，首先介绍了一些李代数的基本知识，并且给出了这两类李代数的组成结构，然后从这两类李代数的本质构成出发，研究它们的一些典型性质，分别讨论了它们的维数，中心，换位子代数，Killing型，Cartan子代数，结构公式，根系等。

We present the fundamental theories of Noether symmetries and conserved quantities of mechanco-electrical dynamical systems, including variation principle of the system, Noether symmetry transformation, Noether quasi-symmetry transformation, generalized Noether quasi-symmetry transformation, Killing equations, Noether theorem, the form of conserved quantity. And then the basic theory of Lie symmetry is advanced, including the determining equation, structure equation and the form of conserved quantity.

给出机电动力系统的Noether对称性和守恒量基本理论，包括系统的变分原理、Noether对称性变换、Noether准对称性变换、广义Noether准对称性变换、Killing方程、Noether定理和守恒量的形式；给出机电动力系统Lie对称性的基本理论，包括确定方程、结构方程以及守恒量的形式。

Let G be semisimple matrix group with Lie algebra g, T a fixed maximal abelian subalgebra of g, T the orthogonal complement of T with respect to the Killing form of g, and a, b 6 T a fixed regular elements.

设G为半单矩阵群，g为其Lie代数，T(来源：ABC论文91网www.abclunwen.com)为g的极大交换子代数，T~⊥为T关于g的Killing型的正交补，a，b∈T为固定正则元。

As well as we introduce some property of Killing form. Finally, we use Killing form to decide if YD-Lie algebras are semisimple.

则称为L的Killing型，以及给出了Killing型的性质，最后用Killing型去判断半单点YD-李代数。

Firstly, we define the Killing form over any finite dimensional Hopf algebras using the adjoint action, then we investigate the fundamental properties of the Killing form, and obtain a decomposition of Hopf algebras under the adjoint action.

首先，利用Hopf代数的伴随作用定义了有限维Hopf代数上的Killing型，并讨论了Killing型的基本性质，得到了Hopf代数上的伴随表示分解式。

Next, we give the definition of Killing form hold for pointed YD-Lie algebra, let L be a pointed YD-Lie algebra, for every homogeneous elements x, y ∈ L, if = tr_q.then we call Killing form of L.

接着，给出了点YD-李代数的Killing型的定义：L为任意的点YD-李代数，如果齐次元x，y∈L定义：=tr_q。

Objective To investigate the effects of interleukin-1 β converting enzyme gene on the biologic characteristics of ovarian cancer cells.

目的 探讨白细胞介素-1 β转换酶的表达，对卵巢癌细胞生物学特性的影响。

Campylobacter: This illness is the most commonly identified cause of diarrheal illness in the world.

弯曲：这种病是最常见的原因查明腹泻病，在世界上。