带作用的群系的临界结构

在本文中，我们讨论了带作用群的群系的临界结构，给出了处理允许某些作用群的群的问题的一般方法，作为应用，我们特别给出了关于幂零群及ｐ－幂零群的一些结果。     

关于有限群的Γ_K类和半惯性子群的一些注记(英文)

本文研究了一个有限群和它的特征标的Galois共轭类.利用群作用和Galois作用,得到了关于相应Γ_K类和半惯性子群的一些结果,推广了一些著名定理.     

基本群在覆盖流形与球面的积空间上的作用

Heitsch在[1]中给出了一些特殊的群作用,并提出了这样的问题:1)与这些群作用相结合的C-代数有何性质?2)相应C-代数与叶状结构有何关系?本文就此进行部分讨论。1 在S~(2k-1)上的群作用     

关于李群胚和泊松作用的讨论

定义了纤维丛的相配群胚的概念,从作用的角度研究了李群胚与主丛的关系;给出了一个泊松群胚在泊松流形上的作用是泊松作用的充要条件;文末得到了一些关于泊松流形上Casimir函数的结果.     

关于群胚作用和李双代数胚态射

在这篇文章中，我们讨论了李双代数胚之间的态射，得到了一些李双代数胚之间态射的性质．研究了泊松群胚在泊松流形上的泊松作用，以及这个泊松作用与被作用流形的切李双代数胚到作用泊松群胚的切李双代数胚之间的态射的关系，得到了一些有用的结论。     

关于低阶K群的若干问题

本文主要介绍了低阶Ｋ群Ｋ＿０，Ｋ＿１，Ｋ＿２及与它们相关的Ｂａｓｓ－Ｑｕｉｌｌｅｎ猜测、Ｂｉｒｃｈ－Ｔａｔｅ猜测研究的最新进展．Ｋ＿０与Ｋ＿１方面主要通过对Ｂａｓｓ～Ｑｕｉｌｌｅｎ猜测研究说明Ｋ＿０，Ｋ＿１的作用，同时也给出了一些多项式环上投射模自同构群的计算公式．在Ｋ＿２群方面，我们主要介绍了域上Ｋ＿２群，代数整数环上Ｋ＿２群以及著名的Ｂｉｒｃｈ－Ｔａｔｅ猜想．并且也给出了Ｋ＿２群一些计算方面的结果．     

有限维线性空间上的极大线性变换群在几个线性空间上的群作用

群作用是研究群(特别是有限群)的一个外部方法.首先构作域上一有限维线性空间上的全线性变换半群的极大群,其次给出了三个群作用:极大群在其幺元的不动点子空间上的一个(自然的)群作用,两个极大群的(外)直积在两个极大群的幺元的不动点子空间的(外)直和上的一个群作用,两个极大群的(外)直积在两个极大群的幺元的不动点子空间之间的所有线性映射构成之集上的一个群作用.     

群可逆元的一些刻画

研究了群可逆元的一些性质,给出群可逆元的一些刻画,进一步研究正则元是群可逆元的若干条件.     

关于CEA-群的探讨

大家知道,从子群具备某些性质来研究群本身,已经成为研究群的一般理论的一个重要方法。这些性质之一是所谓子群的可补性:群 G 的子群 A 称为在群 G 内是可补的,如果在群 G 内存在子群 B,使得 G=AB,并且 A∩B=1。关于具有各类可补子群系的群的研究,已有一批相当数量的成果,其中有一些,已对可补概念本身作了一些推广。本文把可补性定义中的 A∩B 从单位元放宽到初等交换群(即元的阶为同一素数的一次幂的交换群,以及单位元群),引进子群的 EA-可补性及 CEA-群的概念,讨论了 CEA-群的一些性质,并且得出了交换群和幂零群为 CEA-群的充分必要条件。     

关于三维旋转群SO_3

内容 §1.群O_3和SO_3 §2.群SO_3的单性 §3.SO_3与SU_2的关系 §4.群SO_3的自同构 由于三维旋转群SO_3在数学和物理中所起的重要作用,我们在本文中对这个群的一些重要性质作了一个较系统的论述。因为对群SO_3的有限子群的讨论在某些教科书中容易找到,我们在这里将不关心它们。     

Schreier rewriting beyond the classical setting Dedicated to our teacher Alfred Lvovich Shmelkin on his 70th birthday

Using actions of free monoids and free associative algebras, we establish some Schreier-type formulas involving ranks of actions and ranks of subactions in free actions or Grassmann-type relations for the ranks of intersections of subactions of free actions. The coset action of the free group is used to establish a generalization of the Schreier formula in the case of subgroups of infinite index. We also study and apply large modules over free associative and free group algebras.     

Polar actions on Damek-Ricci spaces

A proper isometric Lie group action on a Riemannian manifold is called polar if there exists a closed connected submanifold which meets all orbits orthogonally. In this article we study polar actions on Damek-Ricci spaces. We prove criteria for isometric actions on Damek-Ricci spaces to be polar, find examples and give some partial classifications of polar actions on Damek-Ricci spaces. In particular, we show that non-trivial polar actions exist on all Damek-Ricci spaces.     

Weakly Hyperbolic Actions of Kazhdan Groups on Tori

We study the ergodic and rigidity properties of weakly hyperbolic actions. First, we establish ergodicity for C² volume preserving weakly hyperbolic group actions on closed manifolds. For the integral action generated by a single Anosov diffeomorphism this theorem is classical and originally due to Anosov. Motivated by the Franks/Manning classification of Anosov diffeomorphisms on tori, we restrict our attention to weakly hyperbolic actions on the torus. When the acting group is a lattice subgroup of a semisimple Lie group with no compact factors and all (almost) simple factors of real rank at least two, we show that weak hyperbolicity in the original action implies weak hyperbolicity for the induced action on the fundamental group. As a corollary, we obtain that any such action on the torus is continuously semiconjugate to the affine action coming from the fundamental group via a map unique in the homotopy class of the identity. Under the additional assumption that some partially hyperbolic group element has quasi-isometrically embedded lifts of unstable leaves to the universal cover, we obtain a conjugacy, resulting in a continuous classification for these actions. Partially funded by VIGRE grant DMS-9977371 Received: January 2005 Revision: August 2005 Accepted: September 2005     

On cubic rings and quaternion rings

In this paper, we show that the orbits of some simple group actions parametrize cubic rings and quaternion rings.     

Positivity of direct images of positively curved volume forms

We discuss Kiselman–Berndtsson’s minimum principle for plurisubharmonic functions in terms of the positivity of direct images of certain positively curved volume forms, and generalize it to holomorphically convex manifolds with compact group actions. With this generalization and other techniques, we establish a minimum principle for positively curved volume forms from the point of view of geometric invariant theory on Stein manifolds. Minimum principle with some noncompact group actions is also considered.     

On nilpotent ideals in the cohomology ring of a finite group

In this paper we find upper bounds for the nilpotency degree of some ideals in the cohomology ring of a finite group by studying fixed point free actions of the group on suitable spaces. The ideals we study are the kernels of restriction maps to certain collections of proper subgroups. We recover the Quillen-Venkov lemma and the Quillen F-injectivity theorem as corollaries, and discuss some generalizations and further applications.We then consider the essential cohomology conjecture, and show that it is related to group actions on connected graphs. We discuss an obstruction for constructing a fixed point free action of a group on a connected graph with zero “k-invariant” and study the class related to this obstruction. It turns out that this class is a “universal essential class” for the group and controls many questions about the groups essential cohomology and transfers from proper subgroups.     

Rigidity of Hamiltonian actions on Poisson manifolds

This paper is about the rigidity of compact group actions in the Poisson context. The main result is that Hamiltonian actions of compact semisimple type are rigid. We prove it via a Nash–Moser normal form theorem for closed subgroups of SCI type. This Nash–Moser normal form has other applications to stability results that we will explore in a future paper. We also review some classical rigidity results for differentiable actions of compact Lie groups and export it to the case of symplectic actions of compact Lie groups on symplectic manifolds.     

Globalizations, fiber bundles, and envelopes of holomorphy

We describe a relationship between globalizations of local holomorphic actions on Stein manifolds induced by global actions of certain non-compact Lie groups, and holomorphic fiber bundles with smooth Stein base and fiber and connected structure group. To this end we prove a univalence result for particular Stein Riemann domains with a free and properly discontinuous action of a discrete group of biholomorphisms. We then derive some consequences on the existence of Stein globalizations. Received August 11, 1998; in final form March 8, 1999     

Diffeomorphism classification of finite group actions on disks

In this paper we discuss the diffeomorphism classification of finite group actions on disks. We answer the question when an action on a space M can be extended to an action on a disk such that the action is free away from M. Let the singular set consist of the points with nontrivial isotropy group. We show (under some dimension assumptions) that disks with diffeomorphic neighborhoods of the singular set can be imbedded into each other. As a consequence we find a classification of group actions on disks in terms of the neighborhood of the singular set and an element in the Whitehead group of G.     

Partial actions and partial skew group rings

In this paper we consider partial actions of groups on algebras and partial skew group rings. After some general results we prove two versions of Maschke's theorem and then we study von Neumann regularity, the prime radical and the Jacobson radical of partial skew group rings. In this way we extend many results which are known for skew group rings.