泛代数的二次扩张

在本文中引入了泛代数的二次扩张的概念，解决了ＴＵ－ＥＣ（Ａ）和ＵＴ－ＥＣ（Ａ）的存在、真类和基数问题，范畴ＴＵ－ＥＣ（Ａ）（及ＵＴ－ＥＣ（Ａ）），并得到了有关二次扩张的几个同构定理，还对一点二次扩张作了讨论。     

可解二次Lie代数

一个带有非退化、对称不变双线性型的Lie代数称为二次Lie代数. 研究可解二次Lie代数的结构, 特别是Cartan子代数由半单元构成的可解二次Lie代数. 从上同调的观点出发给出了一种构造二次Lie代数的方法, 并证明了可解二次Lie代数均可用此方法构造.     

交错代数与 Jordan 代数的次理想

在文章[1],[2],[3]中分别对羣,Lie代数和结合环建立了次理想理论。在文章章[4]中对此理论在Lie代数的情形补充了一个定理。一个代数(环,羣)的次理想就是能出现在此代数(环,羣)的某一正规列中的子代数(子环,子羣),亦即,代数R的子代数A是R的次理想,若存在有R的子代数A_i,i=0,1,…,n,使其中n是自然数,A_i是A_(i+l)中的理想,i=0,1,…,n~-1。本文目的在于对交错代数和Jordan代数证明相应理论中的一些定理。即是讨论下面这些问题:什么时候次理想是理想,什么时候次理想之和仍是次理想,什么代数的每一子代数都是次理想,最后,一代数     

具有分解性质的次对角代数

设M是σ-有限的von Neumann代数,21是M的具有分解性质的次对角代数,即对任意可逆算子T∈M,都存在西算子U∈M及可逆算子A∈21∩21~(-1),使得T=UA,本文证明了21的代数换位是自伴的,同时也证明了21中的可逆算子群是σ-弱连通集。     

代数史上的三次真正的进展

在数学的历史上,一些新的有力的工具,更简单方法的发现,往往标志着一个或多个数学分支的产生.数学的发展,是“高级”数学代替“低级”数学的过程.在代数的发展史上有三次真正的进展.大约在30万年前,人类就有了数的概念,但是有文字记载的数学到公元前3400年     

A类算子n次根的代数扩张是次标量算子

研究了A类算子n次根的代数扩张.特别地,利用空间分解技巧得到每个A类算子n次根的代数扩张是次标量算子.作为应用,考虑了此类算子的Weyl型定理和超不变子空间问题.     

Hunt六次曲面的代数研究

对于给定的螺旋3系S，以较初等的代数方法求出由S确定的Hunt六次有界封闭曲面∑．通过三维空间中任一点的螺旋有∞3条，而在∑内任一点，∞3条中属于S的有3条；在∑上任一点，属于S的有两条；在∑外，属于S的仅有一条引入数值例并用计算机绘制出∑的图形．     

Lie超代数及二次Lie超代数的分解惟一性

一个带有非退化超对称不变双线性型的Lie超代数称为二次Lie超代数. 考虑Lie超代数的分解, 得到在同构意义下一个Lie超代数分解为不可分解阶化理想直和的方式惟一及在保距同构意义下一个二次Lie超代数分解为不可约非退化阶化理想直和的方式惟一.     

三次可解型非退化李代数及其导子李代数的结构

本文给出了非退化可解李代数的两个类型:三次可解型非退化李代数和扩充的 Heisenberg李代数,并确定三次可解型非退化李代数及其导子李代数的结构．     

一类时间可逆三次微分系统的代数条件

作者曾给出时间可逆微分系统代数条件推导的算法,并给出了一类时间可逆三次微分系统的系数条件,但其中含有一个实参数.为了消去这个参数,这里使用具有投影性质的三角序列和标准基等消元手段,得到了不含参数的完整代数条件.     

Applications of Algebraic Combinatorics to Algebraic Geometry

We formulate a number of new results in Algebraic Geometry and outline their derivation from Theorem 2.12 which belongs to Algebraic Combinatorics.     

On the Algebraic Cohomology of Real Algebraic M-Varieties

For a real algebraic M-variety X, the canonical homomorphism of the algebraic cohomology group of the set of real points into the algebraic cohomology group of the set of complex points $$\varrho _k :H_{alg}^k (X(\mathbb{R}),\mathbb{Z}/2) \to H_{alg}^{2k} (X(\mathbb{C}),\mathbb{Z}/2)$$ is considered. This homomorphism agrees with the cycle mappings. Estimates for the dimension of the kernel of this homomorphism are given.     

Affine Algebraic Varieties Relative to an Algebraic Theory

Affine algebraic varieties relative to an algebraic theory are introduced and described as irreducible components of affine algebraic sets. Their category is shown to be dually equivalent to the category of irreducible functional algebras.     

Algebraic Holography

. A rigorous (and simple) proof is given that there is a one-to-one correspondence between causal anti-deSitter covariant quantum field theories on anti-deSitter space and causal conformally covariant quantum field theories on its conformal boundary. The correspondence is given by the explicit identification of observables localized in wedge regions in anti-deSitter space and observables localized in double-cone regions in its boundary. It takes vacuum states into vacuum states, and positive-energy representations into positive-energy representations.     

Algebraic stacks

This is an expository article on the theory of algebraic stacks. After introducing the general theory, we concentrate in the example of the moduli stack of vector bundles, giving a detailed comparison with the moduli scheme obtained via geometric invariant theory.     

Algebraic coalitions

The idea of an algebra in is introduced. Within congruence modular varieties such algebras are shown to be the abelian algebras with a one-element subalgebra. This leads on to the notion of algebraic coalition, which is characterized for congruence modular varieties and for varieties of Jónsson–Tarski algebras. This characterization displays an intimate relationship between algebraic coalitions, Gumm difference terms, and the centre of an algebra. Received July 16, 1996; accepted in final form May 2, 1997.     

Algebraic trigonometry

This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos – satisfying an axiom sin²?+?cos²?=?1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two different interpretations of the TF are discussed with many others potentially possible. The main objective of this article is to introduce a broader view of trigonometry that can serve as motivation for mathematics students and teachers to study and teach abstract algebraic structures.     

Algebraic cuts

In this note we give an algebraic version of a construction called symplectic cutting, which is due to Lerman. Our construction is valid for projective varieties defined over arbitrary fields. Using the equivariant intersection theory developed by the authors, it is a useful tool for studying quotients by torus actions. At the end of the paper, we give an algebraic proof of the Kalkman residue formula and use it to give some formulas for characteristic numbers of quotients.