关于Chevalley群扩群的两点继续研究

构造出Ｄ２ｍ型Ｃｈｅｖａｌｌｅｙ群扩群Ｇ,证明了其唯一性,并讨论了文「１」中构造的Ａｎ型Ｇ的唯一性。     

p-adic域上Chevaley群的Harish-Chandra同态的注记

设Ｇ为ｐ┐ａｄｉｃ域Ｆ上典型Ｃｈｅｖａｌｅｙ群且Ｆ′为Ｆ的扩充，设Ｇ′为定义在Ｆ′上Ｇ的抛物子群的Ｌｅｖｉ因子，给出了Ｇ的高同余球函数代数到Ｇ′的高同余球函数代数的Ｈａｒｉｓｈ┐Ｃｈａｎｄｒａ同态．这是对Ｆ上群ＧＬｎ在同样情况下的高同余球函数代数的Ｈａｒｉｓｈ┐Ｃｈａｎｄｒａ同态的推广．     

2pq阶群的自同构群

继续「１～２」等的工作,给出了２ｐｑ阶群Ｇ的自同构群ＡｕｔＧ的准确构造。     

群代数作用遍历性的一点注记

证明了由自由群整数环上一类元素确定的代数作用的遍历性,计算了Heisenberg群因子中特定元素的Fuglede-Kadison行列式值.     

环Z2l上广义Bent函数的稳定性

文献「４」为研究密钥流序列的线性复杂度稳定性和使一些流密码能抗ＢＡＡ（最佳仿射逼近）攻击,提出Ｂｅｎｔ函数稳定性概念,文献「７」研究了素域Ｚｐ上广义Ｂｅｎｔ函数的稳定性及其构造,并指出当ｍ是合数时,ｍ值广义Ｂｅｎｔ函数并不都有稳定性,本文进一步在环Ｚ２＾ｌ（ｌ〉１）上提出了广义Ｂｅｎｔ函数稳定性的概念,综合应用谱、概率和代数数论的方法考察了稳定的概率意义,给出了稳定函数的概率判别条件,提供了构造稳     

一类整除性定理的推广

「１」给出复数Ｃ上多元多项式环Ｃ「ｘ１,ｘ２,…,ｘｎ」的一类整除性定理,本把它推广为任意代数闭域ｋ上多元多项式环ｋ「ｘ１,ｘ２,…,ｘｎ」的情形。     

环的Galois,分离和Frobenius扩张

设∧是其中心Ｃ＿∧上的有限维单代数，Ｆ是满足Ｃ＿∧的∧的子环，Ｇ是保持Γ的元素不变的∧的自同构的有限群．本文证明：若∧／Γ是Ｇ－Ｇａｌｏｉｓ扩张，则在∧中的中心化子△是Ｃ＿Γ一分离代数且∧／Γ是Ｆｒｏｂｅｎｉｕｓ扩张，这里Ｃ＿Γ是Γ的中心．     

分次FS—环

本文引进群分次环上分次模的分次ＦＳ－模的概念,利用分次极大分次左理想给出分次ＦＳ－环的几个刻画,得到了环Ｒ和群环ＲＧ,分次环Ｒ和分次环的群环Ｒ「Ｇ」间的几个等价条件。     

布尔代数上的线性群

布尔代数上的线性群罗铸楷，刘任任（湘潭大学计算机科学系，湘潭４１１１０５）ＯＮＬＩＮＥＡＲＧＲＯＵＰＳＯＶＥＲＢＯＯＬＥＡＮＡＬＧＥＢＲＡ￥ＬＵＯＺＨＵＫＡＩ（ＬｏＣＺＵＫＡＩ）；ＬＩＵＲＥＮＲＥＮ（ＤｅｐａｒｔｍｅｎｔｏｆＣｏｍｐｕｔｅｒＳｃｉｅｎ...     

Hilbert空间上全纯映照的角导数

设Ｆ（ｚ）为Ｈｉｌｂｅｒｔ空间上的半平面ＨＣ到ＨＣ的全纯映照,本文我们研究保证Ｆ（Ｚ）的角导数存在的条件,在「３」中定理相同的假设下我们得到了更强的结论。     

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     

Complete radicals of some group rings

We continue studying the associative rings complete and reduced in the sense of Martynov. We prove that the group of invertible elements of a reduced associative ring is reduced. We compute the complete radical of a group ring over the ring of integers and the complete radical of the group algebra over an arbitrary algebra over a finite prime field.     

AUTOMORPHISMS OF THE ENVELOPING ALGEBRA OF THE THREE-DIMENSIONAL NILPOTENT LIE ALGEBRA

We prove that the group of tame automorphisms of the universal enveloping algebra of the three-dimensional nilpotent nonabelian Lie algebra over a field of characteristic 0 is dense with respect to the formal power series topology in the group of all automorphisms.

     

Some Remarks on Absolute Mathematics

We calculate Hochschild cohomology groups of the integers treated as an algebra over so-called field with one element. We compare our results with calculation of the topological Hochschild cohomology groups of the integers—this is the case when one considers integers as an algebra over the sphere spectrum.     

关于自正交的整表代数码

整表代数是群代数的推广，它的理想是群代数码的推广．本文给出了整表代数的单边理想是自正交理想的必要充分条件．     

Local models of Shimura varieties and a conjecture of Kottwitz

We give a group theoretic definition of “local models” as sought after in the theory of Shimura varieties. These are projective schemes over the integers of a p-adic local field that are expected to model the singularities of integral models of Shimura varieties with parahoric level structure. Our local models are certain mixed characteristic degenerations of Grassmannian varieties; they are obtained by extending constructions of Beilinson, Drinfeld, Gaitsgory and the second-named author to mixed characteristics and to the case of general (tamely ramified) reductive groups. We study the singularities of local models and hence also of the corresponding integral models of Shimura varieties. In particular, we study the monodromy (inertia) action and show a commutativity property for the sheaves of nearby cycles. As a result, we prove a conjecture of Kottwitz which asserts that the semi-simple trace of Frobenius on the nearby cycles gives a function which is central in the parahoric Hecke algebra.     

Scaling Invariants and Symmetry Reduction of Dynamical Systems

Scalings form a class of group actions that have theoretical and practical importance. A scaling is accurately described by a matrix of integers. Tools from linear algebra over the integers are exploited to compute their invariants, rational sections (a.k.a. global cross-sections), and offer an algorithmic scheme for the symmetry reduction of dynamical systems. A special case of the symmetry reduction algorithm applies to reduce the number of parameters in physical, chemical or biological models.