关于整表代数的同构

对任意整表基为T 的整表代数, 研究了代数整数环的一个子环R上的整R-代数RT, 证明了两个整表代数之间的一个R-代数同构必是一个整表代数同构, 只要它与一种标准化变换相容.     

整代数体函数与其导函数的增长级

对整代数体函数与其导函数的增长性进行了研究,得到了整代数体函数与其导函数的特征函数之间关系式,并证明了它们具有相同的级和下级,从而将亚纯函数的相应结果推广到了整代数体函数.     

两类整环在w-算子下的刻画

通过对SM整环中准素w-理想与w-互素理想的讨论,证明了R是Krull整环当且仅当R是SM整环,w-dim(R)=1,且每个p-准素w-理想是素理想p的幂的w-包络.同时,运用w-算子,辅以t-,v-算子给出了π-整环的一些新的等价刻画.     

保矩阵{1}逆的线性映射

设R是特征为2的主理想整环,Mn(R)表示R上n×n矩阵代数,在本文中我们给出了保Mn(R)中矩阵{1}逆的线性映射的一个刻划.     

整系数多项式有理根定理的改进

文章对整系数多项式有理根定理进行了推广和改进．运用本文的定理，可使整系数多项式有理根的寻求变得简便易行．     

主理想整环上的线性方程组的通解

将文[1]中整数环上的线性方程组问题推广到主理想整环上,利用主理想整环上的矩阵的初等变换及等价标准形导出了主理想整环上的线性方程组有解的一个充分必要条件和求解方法.最后,通过实例说明了算法.     

Borel的一个定理的一个应用

在这篇论文中，研究了一般形式的代数微分方程的亚纯解的增长性并得到一些结果，研究的方法是根据一个关于亚纯函数组的定理。这个定理是Ｂｏｒｅｌ的一个关于整函数组的定理的一个推广。     

关于R~n中Mbius变换群的代数有限性

本文推广了Ｅｉｃｈｌｅｒ在Ｋｌｅｉｎ群的研究中所采用的上同调方法，对于Ｒｎ中的Ｍｂｉｕｓ变换群引进更为一般的线性上同调空间的概念．在此基础上，将作者早期的工作加以推广，研究Ｒｎ中Ｍｂｉｕｓ变换群的代数有限性，并作为特例给出高维Ｋｌｅｉｎ群有限性的一种代数判据．     

整系数多项式有理根定理的改进

文章对整系数多项式有理根定理进行了推广和改进．运用本文的定理，可使整系数多项式有理根的寻求变得简便易行．     

BCC-代数与整偏序幺半群

本文研究ＢＣＣ-代数与整偏序幺半群的关系,所得结果是Ｉ．Ｆｌｅｉｓｃｈｅｒ在［２］中相应结果的推广．     

On isomorphisms of integral table algebras

For integral table algebras with integral table basisT, we can consider integralR-algebraRT over a subringR of the ring of the algebraic integers. It is proved that anR-algebra isomorphism between two integral table algebras must be an integral table algebra isomorphism if it is compatible with the so-called normalizings of the integral table algebras     

幂零表代数

本文研究了幂零表代数的一个有趣的性质,利用表代数的Jordan-Hlder型定理,证明了表代数满足幂零被幂零扩张仍是幂零的,但有限幂零群没有这样的扩张.     

Normalized integral table algebras generated by a faithful real element of degree 2 and having 4 linear elements

We completely classify the normalized integral table algebra (A, B) generated by a faithful real element of degree 2 and having four linear elements.     

On Even Generalized Table Algebras

Generalized table algebras were introduced in Arad, Fisman and Muzychuk (Israel J. Math. 114 (1999), 29–60) as an axiomatic closure of some algebraic properties of the Bose-Mesner algebras of association schemes. In this note we show that if all non-trivial degrees of a generalized integral table algebra are even, then the number of real basic elements of the algebra is bounded from below (Theorem 2.2). As a consequence we obtain some interesting facts about association schemes the non-trivial valencies of which are even. For example, we proved that if all non-identical relations of an association scheme have the same valency which is even, then the scheme is symmetric.     

Common properties of table algebras and association schemes

The concept of table algebra in the title is a real nonsingular generalized table algebra in the sense of [Z. Arad, E. Fisman, M. Muzychuk, Generalized table algebras, Israel J. Math. 114 (1999) 29–60]. In this paper we first give some definitions and facts about table algebras. It is well known that every association scheme gives a Hecke-algebra which is a table algebra too. This leads to the natural question which properties of association schemes stay valid for table algebras. For instance, we prove the Second Isomorphism Theorem and the Jordan–Holder's theorem for standard table algebras.     

Association Schemes and Fusion Algebras (An Introduction)

We introduce the concept of fusion algebras at algebraic level, as a purely algebraic concept for the fusion algebras which appear in conformal field theory in mathematical physics. We first discuss the connection between fusion algebras at algebraic level and character algebras, a purely algebraic concept for Bose-Mesner algebras of association schemes. Through this correspondence, we establish the condition when the matrix S of a fusion algebra at algebraic level is unitary or symmetric. We construct integral fusion algebras at algebraic level, from association schemes, in particular from group association schemes, whose matrix S is unitary and symmetric. Finally, we consider whether the modular invariance property is satisfied or not, namely whether there exists a diagonal matrix T satisfying the condition (ST)³ = S ². We prove that this property does not hold for some integral fusion algebras at algebraic level coming from the group association scheme of certain groups of order 64, and we also prove that the (nonintegral) fusion algebra at algebraic level obtained from the Hamming association scheme H(d, q) has the modular invariance property.     

标度广义效应代数和标度效应代数的结构

研究了标度广义效应代数与标度效应代数的代数结构,给出了比较完整的结果.通过引入全标度广义代数的概念,本文证明了区间[0,1)上的标度广义效应代数和单位区间[0,1]上的标度效应代数完全由单位区间上的阿基米德余模确定,标度广义效应代数恰同构于全标度广义代数的下集.若标度广义代数满足局部有限条件,则它同构于实数加法群的子群代数.满足(S)条件的标度效应代数同构于实数加法群的子群代数和全标度广义代数的字典序乘积的子代数.     

Stably Calabi-Yau algebras and skew group algebras

Let G be a finite group and A be a finite-dimensional selfinjective algebra over an algebraically closed field. Suppose A is a left G-module algebra. Some suficient conditions for the skew group algebra AG to be stably Calabi-Yau are provided, and some new examples of stably Calabi-Yau algebras are given as well.     

Lie Representations and an Algebra Containing Solomon's

We introduce and study a Hopf algebra containing the descent algebra as a sub-Hopf-algebra. It has the main algebraic properties of the descent algebra, and more: it is a sub-Hopf-algebra of the direct sum of the symmetric group algebras; it is closed under the corresponding inner product; it is cocommutative, so it is an enveloping algebra; it contains all Lie idempotents of the symmetric group algebras. Moreover, its primitive elements are exactly the Lie elements which lie in the symmetric group algebras.     

Construction of Rota-Baxter algebras via Hopf module algebras

We propose the notion of Hopf module algebra and show that the projection onto the subspace of coinvariants is an idempotent Rota-Baxter operator of weight-1. We also provide a construction of Hopf module algebras by using Yetter-Drinfeld module algebras. As an application,we prove that the positive part of a quantum group admits idempotent Rota-Baxter algebra structures.