幂幺矩阵的谱分解与幂幺指数的确定

给出了不需要求出特征值和特征向量的幂幺矩阵的谱分解的计算公式,并得到了幂幺指数的确定方法.这不仅推广改进了已有幂幺指数的一些性质,而且还得到了两个幂幺矩阵相似的判定条件.     

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.     

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。     

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.     

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.     

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。     

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.     

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．     

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.     

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.     

Remarks on the Transfer Factors for Unipotent Orbital Integrals in p-adic Classical Split Groups

This article studies unipotent orbital integrals on symplectic and orthogonal groups from the point of view of endoscopy. It begins by partitioning stable unipotent classes into packets and goes on to propose a transfer of these packets. It then discusses (in rough form) the associated transfer factors. Some supporting calculations in split odd orthogonal groups are given.     

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.     

Unipotent Brauer Character Values of GL(n, \mathbb{F}_q ) and the Forgotten Basis of the Hall Algebra

We give a formula for the values of irreducible unipotent p-modular Brauer characters of at unipotent elements, where p is a prime not dividing q, in terms of (unknown!) weight multiplicities of quantum GL _n and certain generic polynomials S _,(q). These polynomials arise as entries of the transition matrix between the renormalized Hall-Littlewood symmetric functions and the forgotten symmetric functions. We also provide an alternative combinatorial algorithm working in the Hall algebra for computing S _,(q).     

Unipotent Elements in Small Characteristic, II

Let G be a special orthogonal group over an algebraically closed field of characteristic exponent p. In this paper we extend certain aspects of the Dynkin–Kostant theory of unipotent elements of G (when p?=?1) to the general case (including p?=?2).     

F-isocristaux unipotents

We show that unipotent overconvergent isocrystals are algebraic and that the category of unipotent overconvergent isocrystals has a Frobenius automorphism. We also prove a structure theorem for unipotent overconvergent F-isocrystals over an open subset of the line, analogous to Dieudonné–Manin decomposition theorem for F-isocrystals.     

Skew Linear Unipotent Groups

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

Large Abelian Unipotent Subgroups of Finite Chevalley Groups

We compute maximal orders of unipotent Abelian subgroups, estimate p-ranks, and describe the structure of Thompson subgroups of maximal unipotent subgroups of finite exceptional groups of Lie type.     

Galois Cohomology of Unipotent Algebraic Groups and Field Extensions

In this note we discuss, in the case of unipotent groups over nonperfect fields k of characteristic p, an analog of a theorem of Steinberg (formely a Serre's conjecture) for unipotent algebraic group schemes, which relates properties of Galois (or flat) cohomology of unipotent group schemes to finite extensions of k of degree divisible by p.