An Algorithm for the Modular Decomposition of Hypergraphs

We propose an O(n⁴) algorithm to build the modular decomposition tree of hypergraphs of dimension three and show how this algorithm can be generalized to compute in O(n^{3k − 5}) time the decomposition of hypergraphs of any fixed dimension k.     

Hypercentral Unit Groups and the Hyperbolicity of a Modular Group Algebra

We classify groups G such that the unit group 𝒰 ₁(? G) is hypercentral. In the second part, we classify groups G whose modular group algebra has hyperbolic unit groups 𝒰 ₁(KG).     

Decomposition for Complex Clifford Algebra of Even Dimension

In this paper we consider several fundamental operators in complex Clifford algebra and show the close relationship of these operators. We also discuss a representation of the Lie algebra s[（z; C） and get several decompositions for Clifford algebra of even dimension under the action of these fundamental operators.     

A Decomposition of the Descent Algebra of a Finite Coxeter Group

The purpose of this paper is twofold. First we aim to unify previous work by the first two authors, A. Garsia, and C. Reutenauer (see [2], [3], [4], [5] and [10]) on the structure of the descent algebras of the Coxeter groups of type A _n and B _n. But we shall also extend these results to the descent algebra of an arbitrary finite Coxeter group W. The descent algebra, introduced by Solomon in [14], is a subalgebra of the group algebra of W. It is closely related to the subring of the Burnside ring B(W) spanned by the permutation representations W/W _J, where the W _J are the parabolic subgroups of W. Specifically, our purpose is to lift a basis of primitive idempotents of the parabolic Burnside algebra to a basis of idempotents of the descent algebra.     

Efficient and Practical Algorithms for Sequential Modular Decomposition

A module of an undirected graph G = (V, E) is a set X of vertices that have the same set of neighbors in V\X. The modular decomposition is a unique decomposition of the vertices into nested modules. We give a practical algorithm with an O(n + mα(m, n)) time bound and a variant with a linear time bound.     

关于高等代数中根子空间分解定理的教学

通过改进定理的证明、对定理进行推广、增加例题和习题等方法,改进高等代数中线性空间的根子空间分解定理的教学.     

基于共形几何代数的几何分解及程序实现

本文主要讨论了利用共形几何代数来进行几何定理中的几何构型进行几何分解的算法以及它的程序实现问题.利用这个算法可以给出几何量之间的定量依赖关系.所实现的程序能够给出一些较为复杂的几何命题的自动分解的结果.     

The Direct Sum Decomposition of Type G_2 Lie Algebra

This article mainly discusses the direct sum decomposition of type G_2 Lie algebra, which, under such decomposition, is decomposed into a type A_1 simple Lie algebra and one of its modules. Four theorems are given to describe this module,which could be the direct sum of two or three irreducible modules, or the direct sum of weight modules and trivial modules, or the highest weight module.     

无限维Κ型单模李超代数及其超导子代数

首先证明了无限维K(m,n)型模李超代数的单性,给出了它的生成元集,进而通过导子在生成元上的作用,确定了它的Z-齐次超导子,最后确定了K(m,n)的齐次超导子代数.     

可换环上上三角矩阵代数的若当自同构分解

设R是含单位元1和可逆元2的可换环,Tn+1(R)表示R上(n+1)×(n+1)级上三角矩阵全体所形成的矩阵代数.本文证明了T(R)的每一个若当自同构都可唯一的分解为图自同构,内自同构和对角自同构的乘积.     

Decomposition of Modular Codes for Computing Test Sets and Graver Basis

In order to obtain the set of codewords of minimal support for codes defined over ${\mathbb{Z}_q}$ , one can compute a Graver basis of the ideal associated to such codes. The main aim of this article is to reduce the complexity of the algorithm obtained by the authors in a previous work taking advantage of the powerful decomposition theory for linear codes provided by the decomposition theory of representable matroids over finite fields. In this way we identify the codes that can be written as ??gluing?? of codes of shorter length. If this decomposition verifies certain properties then computing the set of codewords of minimal support in each code appearing in the decomposition is equivalent to computing the set of codewords of minimal support for the original code. Moreover, these computations are independent of each other, thus they can be carried out in parallel for each component, thereby not only obtaining a reduction of the complexity of the algorithm but also decreasing the time needed to process it.     

具有三角分解李代数的积分元和中心扩张

本文将应用广义限制李代数的概念来研究具有三角分解李代数的积分元和中心扩张的关系.对于给定的广义限制普遍包络代数,我们确定了它的积分元并且提供了一种计算dim H2(L,F)的方法.     

Decomposition of Jordan Automorphisms of Strictly Upper Triangular Matrix Algebra Over Commutative Rings

Over a 2-torsionfree commutative ring R with identity, the algebra of all strictly upper triangular n + 1 by n + 1 matrices is denoted by n ₁. In this article, we prove that any Jordan automorphism of n ₁ can be uniquely decomposed as a product of a graph automorphism, a diagonal automorphism, a central automorphism and an inner automorphism for n ≥ 3. In the cases n = 1, 2, we also give a decomposition for any Jordan automorphism of n ₁.     

Witt代数和Virasoro代数上的Poisson代数结构

Poisson代数是指同时具有结合代数结构和李代数结构的一类代数,其结合代数结构和李代数结构满足Leibniz法则.确定了特征为0和特征为p>0的基域上的Witt代数和Virasoro代数上的Poisson代数结构.     

一类Witt代数的包络代数的表示

设C为复数域,P,q∈C,且pq是m次本原单位根．我们构造了一个Zm-分次模类V(a,b),它为Witt代数的包络代数的(P,q)变形U(Wpq)的Zm-分次模类,并证明了任何一个Zm-分次U(Wpq)-模都与某个V(a,b)同构．     

Hall Numbers and the Composition Algebra of the Kronecker Algebra

We present formulas for the structure constants (Hall numbers) of the Hall algebra associated to the Kronecker algebra. The formulas which in some cases involve the classical Hall polynomials enable us to determine every Hall number. Using again these formulas we construct new PBW-bases with simple structure constants for the composition algebra , making possible the definition of the generic composition algebra via Hall polynomials.Presented by C. Ringel.     

扭Heisenberg-Virasoro代数上Hom-李代数结构

Hom-李代数是一类满足反对称和Hom-Jacobi等式的非结合代数.扭Heisenberg-Virasoro代数是次数不超过1的微分算子代数的中心扩张,它是一类重要的无限维李代数,与一些曲线的模空间有关.文章主要研究扭Heisenberg-Virasoro代数上Hom-李代数结构,确定了扭Heisenberg-Virasoro代数上存在非平凡的Hom-李代数结构.