辫子群的全部二维不可约表示

通过直接解矩阵方程给出了Bn群的全部二维不可约表示．     

局部环上正交群中一类子群的扩群

定出了局部环上正交群中一类子群的扩群,得到了如下结果:设R是局部环,M是R的唯一极大理想,O(2m,R)为R上正交群.对R的任意理想S,G(2m,S)表示子群{A BC D∈O(2m,R)|B∈Sm×m}.如果char(R)≠2,m≥3,G(2m,0)≤X≤G(2m,M),那么存在R的理想S,使得X=G(2m,S).     

Flat Modules over Group Rings of Finite Groups

Let k be a commutative ring of coefficients and G be a finite group. Does there exist a flat k G-module which is projective as a k-module but not as a k G-module? We relate this question to the question of existence of a k-module which is flat and periodic but not projective. For either question to have a positive answer, it is at least necessary to have |k| ≥ ?_ω. There can be no such example if k is Noetherian of finite Krull dimension, or if k is perfect.     

二面体群的Grothendieck环结构

二面体群的表示范畴为对称半单monoidal范畴,因而其Grothendieck环为有限多个元素生成的交换环.本文确定了该Grothendieck环的极小生成元,并且进一步证明了该Grothendieck环与某一多项式环的商环同构.     

二面体群的Grothendieck环结构

二面体群的表示范畴为对称半单monoidal范畴,因而其Grothendieck环为有限多个元素生成的交换环.本文确定了该Grothendieck环的极小生成元,并且进一步证明了该Grothendieck环与某一多项式环的商环同构.     

Quasi-Invariant Measures and Irreducible Representations of the Inductive Limit of Special Linear Groups

Unitary representations of the group are constructed. The construction uses G-quasi-invariant measures on some G-spaces that are subspaces of the space of two-way infinite real matrices. We give a criterion for the irreducibility of these representations.     

Deformation of Irreducible Unitary Representations of Discrete Series of Hermitian Symmetric Simple Lie Groups in the Class of Pure Pseudorepresentations

Mathematical Notes -     

Rings and constructions of partial difference sets

We present three constructions of partial difference sets (PDS) using different types of finite local rings. The first construction uses homomorphic images of finite Frobenius local rings and generalizes a previous result by the author. The second construction uses finite Frobenius local rings. The third construction uses finite (noncommutative) chain rings and generalizes a recent construction of partial difference sets by Leung and Ma. The three constructions provide many new PDS in nonelementary abelian groups.     

Isomorphisms of the Unitriangular Groups and Associated Lie Rings for the Exceptional Dimensions

Isomorphisms between finitary unitriangular groups and those of associated Lie rings are studied. In this paper we investigate exceptional cases. Mathematics Subject Classifications (2000) 16W20, 20H25.     

Globally Irreducible Representations of Finite Groups and Integral Lattices

The notion of globally irreducible representations of finite groups has been introduced by B. H. Gross, in order to explain new series of Euclidean lattices discovered recently by N. Elkies and T. Shioda using Mordell--Weil lattices of elliptic curves. In this paper we first give a necessary condition for global irreducibility. Then we classify all globally irreducible representations of L ₂(q) and ²B₂(q), and of the majority of the 26 sporadic finite simple groups. We also exhibit one more globally irreducible representation, which is related to the Weil representation of degree (pⁿ-1)/2 of the symplectic group Sp_2n(p) (p 1 (mod 4) is a prime). As a consequence, we get a new series of even unimodular lattices of rank 2(pⁿ–1). A summary of currently known globally irreducible representations is given.     

单因环的性质、等价条件和结构

一个有单位元的结合环，如果其元素不是单位就是零因子，则称其为单因环。它是很广泛的一个环类．本文讨论了单因环的住质、等价条件和结构；还讨论了它同其它环诸如正则环、局部环和循环环的关系，从而较深刻地刻划了这种环。     

A Note on Rings and Modules Graded by Some Special Groups

In this note we prove that the prime madicals of some graded rings and the scoles of some graded modules are also graded. The results on the relations between the prime radical and the graded prime radical are also presented. Moreover, the relations between a graded ring and its initial subring are studied.     

Local Subgroups and Group Algebras of Finite p-Solvable Groups

Let p be a prime, k an algebraically closed field ofcharacteristic p, and G a finite group with a Sylowp-Subgroup P. In this paper, we consider the property thatNG(P)/P is Abelian. We provide somenecessary or sufficient conditions NG(P)/P to be Abelian in term of thestructure of the group algebra kG as a k-algebra, in casethat G is p-nilpotent or of p-length 1.     

A Note on Bruhat Decomposition of GL(n) over Local Principal Ideal Rings

Let A be a local commutative principal ideal ring. We study the double coset space of GL _n (A) with respect to the subgroup of upper triangular matrices. Geometrically, these cosets describe the relative position of two full flags of free primitive submodules of A ⁿ . We introduce some invariants of the double cosets. If k is the length of the ring, we determine for which of the pairs (n,k) the double coset space depends on the ring in question. For n = 3, we give a complete parametrisation of the double coset space and provide estimates on the rate of growth of the number of double cosets.     

欧氏环上特殊正交群的一类极大子群

定出欧氏环上特殊正交群的一类极大子群,得到如下结果:设R是带有欧氏映射σ的特征不为2的欧氏环且不是域,SO(2m,R)为R上的特殊正交群,R*=R\{0},l=min{σ(x)|x∈R*\U(R)},任取a∈R*\U(R)使σ(a)=l,记a在R中生成的主理想为M.那么当m≥3时,AB CD∈SO(2m,R)|B∈Mm×m是SO(2m,R)的一个极大子群.     

有限特殊射影酉群U_4(q)与U_5(q)的一个特征性质

间; 设G为有限群,如对每个质数r都有那么 此处 n=4或5,