幂幺矩阵的幂幺指数

引入了幂幺矩阵的幂幺指数的概念,得到了幂幺指数的若干性质,进一步刻画了幂幺矩阵的性质特征.     

幂幺矩阵的充要条件

研究幂幺矩阵的充要条件,利用矩阵的秩和齐次线性方程组解空间的维数.将m=2时幂幺矩阵的充要条件推广到一般幂幺矩阵的充要条件,得出了幂幺矩阵可对角化的结果,并将幂幺矩阵的充要条件平行地推广到幂幺线性变换.     

幂等元位于中心的半群的局部化和最小幂幺半群同余

局部化是交换代数的重要工具[1],证明幂等元位于中心的半群在其幂等元半格上的局部化存在且唯一,并给出此类半群的最小幂幺半群同余.另外,给出了若干半群的重要同余的刻划.     

由n次幂等矩阵确定的交换幺半群

设R是含幺结合环,n≥2为自然数.对所有的k≥1,本文给出了n次幂等矩阵集Pk^n（R）={P｜P^n=P∈Mk（R）}上的一种等价关系,证明了P^n（R）=∪k=1^∞Pk^n（R）中的等价类在给定的加法运算下构成一个交换幺半群.     

C3中的全纯幂幺Jacobian猜想

证明当n=3时,全纯幂幺Jacobian猜想成立.     

幺半群上的Rees矩阵半群的半格的结构

推广了Ｍ．Ｐｅｔｒｉｃｈ在文「１」中所用的方法，得到了幺半群上Ｒｅｅｓ矩阵半群的半格的一个结构定理，研究了单幂幺半群Ｒｅｅｓ矩阵半群的半格的性质并给出了矩形单幂幺半群的半格的若干等价刻划。     

广义m-幂矩阵的等价条件

利用矩阵的秩和齐次线性方程组解空间的维数,给出了广义m-幂矩阵的5个等价条件,推广了幂幺矩阵和m次幂等矩阵的相应结论.此外,把广义m-幂矩阵的这几个等价条件推广到了广义m-幂变换中.     

幂等右侧Quantale上的幂零矩阵

讨论幂等右侧Quantale上的幂零矩阵的若干性质，给出了幂等右侧Quantale上的矩阵为幂零矩阵的充要条件，得到了幂零矩阵的幂零指数的刻画定理。     

半群上Rees矩阵半群的半格的结构

推广了Ｍ．Ｐｅｔｒｉｃｈ在文［１］中所用的方法，得到了幺半群上Ｒｅｅｓ矩阵半群的半格的一个结构定理．研究了单幂幺半群上Ｒｅｅｓ矩阵半群的半格的性质并给出了矩形单幂幺半群的半格的若干等价刻划．     

广义(u,v)幂等矩阵

首先定义了一类新的矩阵一广义(u,v)幂等矩阵,然后研究了它的等价刻画,从而推广了(u,v)幂等矩阵、m幂幺矩阵、m幂等矩阵的一些相应结果.此外,也探讨了广义(u,v)幂等矩阵的性质,以及广义(u,v)幂等矩阵与广义m幂矩阵的关系.     

Skew Linear Unipotent Groups

A unipotent linear group over a skew field of characteristic2 is nilpotent. 2000 Mathematics Subject Classification 20H25(primary), 20F18 (secondary).     

Unipotent elements in small characteristic

Let G be a reductive connected algebraic group over an algebraically closed field of characteristic exponent p ≥ 1. One of the aims of this paper is to present a picture of the unipotent elements of G which should apply for arbitrary p and is as close as possible to the picture for p = 1. Another aim is the study of B_u, the variety of Borel subgroups of G containing a unipotent element u. It is known [Sp] that when p is a good prime, the l-adic cohomology spaces of B_u are pure. We would like to prove a similar result in the case where p is a bad prime. We present a method by which this can be achieved in a number of cases.     

On Fusion in Unipotent Blocks

The context of this note is as follows. One considers a connectedreductive group G and a Frobenius endomorphism F: G G definingG over a finite field of order q. One denotes by G^F the associated(finite) group of fixed points. Let l be a prime not dividing q. We are interested in the l-blocksof the finite group G^F. Such a block is called unipotent ifthere is a unipotent character (see, for instance, [6, Definition12.1]) among its representations in characteristic zero. Roughlyspeaking, it is believed that the study of arbitrary blocksof G^F might be reduced to unipotent blocks (see [2, Théorème2.3], [5, Remark 3.6]). In view of certain conjectures aboutblocks (see, for instance, [9]), it would be interesting tofurther reduce the study of unipotent blocks to the study ofprincipal blocks (blocks containing the trivial character).Our Theorem 7 is a step in that direction: we show that thelocal structure of any unipotent block of G^F is very close tothat of a principal block of a group of related type (notionof ‘control of fusion’, see [13, 49]). 1991 MathematicsSubject Classification 20Cxx.     

Generalized Quivers for Locally Unipotent Rings

In this article, we generalize the definition of a Gabriel quiver in order to provide an analogous combinatorial object for the study of certain locally Artinian rings. We are then able to extend Gabriel's Theorem to locally unipotent rings whose generalized left and right quivers are trees.     

Unipotent groups associated to reduced curves

Let be a curve defined over an algebraically closed field with 0$">. Assume that is reduced. In this paper we study the unipotent part of the Jacobian . In particular, we prove that if is large in terms of the dimension of , then is isomorphic to a product of additive groups .

     

Supercharacters of Unipotent and Solvable Groups

The notion of the supercharacter theory was introduced by P. Diaconis and I. M. Isaaks in 2008. In this paper, we present a review of the main notions and facts of the general theory and discuss the construction of the supercharacter theory for algebra groups and the theory of basic characters for unitriangular groups over a finite field. Based on his earlier papers, the author constructs the supercharacter theory for finite groups of triangular type. The structure of the Hopf algebra of supercharacters for triangular groups over finite fields is also characterized.