四维不定空间中晶体群的分类

设V是四维不定空间，W是V中某个不可约根系的无限Weyl群，本文给出了点群为W的晶体群在仿射群A（V）中的共轭类。     

双曲型5-维不定空间中晶体群的分类

设V是双曲型5-维不定空间，W是V中某个不可约根系的无限Weyl群。本文中，我们在仿射群A(V)中共轭的意义下，给出了点群为W的晶体群的分类。     

关于Weyl群的某些研究

记 Φ为欧氏空间 V中某不可约根系 ,具有 Weyl群 W,记 σ为 W中满足条件 w( Φ+ ) =Φ-的唯一元 .本文考虑如何将 σ分解成反射之积 ;σ在 Φ上的作用方式如何 .作为应用确定了 W的中心 ;进一步确定了 V的一类子空间在 W中的固定子群 .     

关于非齐次线性方程组解的结构的进一步讨论

一、子空间的陪集定义1.设V是数域F上的向量空间,W是V的子空间。若v是V中任意向量,把和v w(w∈W)组成的集记作v W,即v W={v w|w∈W},则这些集称为V中W的陪集。 容易证明下面定理 定理1.V中W的陪集将V分成互不相交的集,即:(ⅰ)任何两个陪集u W与v W或重合或不相交;(ⅱ)每个v∈V属于一个陪集,事实上v∈v W     

三角代数上Lie三重导子的刻画

设u=Tri(A,M,B)是三角代数.证明了在一般的假设下,如果线性映射δ:u→u,满足对任意的U,V,W∈u且UV=UW=0(或U·V=U·W=0),有δ([[U,V],W])=[[δ(U),V],W]+[[U,δ(V)],W]+[[U,V],δ(W)],则对任意U∈u,δ(U)=φ(U)+h(U),其中φ:u→u是一个导子,线性映射h:u→Z(u),满足对任意的U,V,W∈u且UV=UW=0(或U·V=U·W=0),有h([[U,V],W])=0.     

分次Morita Contexts与分次根

设M={A=⊕_(g∈G)A_g,V=⊕_(g∈G)V_g,W=⊕_(g∈G)W_g,B=⊕_(g∈G)B_g}与(,),[,]是一个G-分次Morita Context,且满足(V,W)=A,[W,V]=B,A,B都有单位元．本文证明τG(B)：[W,ΥG(A)V]=【WΥc(A),V],ΥG(A)=(V,ΥG(B)W)=(VΥG(B),W)其中ΥG代表P_G(分次素根),J_G(分次Jacobson根),K_G(分次Koethe根),L_G(分次Levitzki根)和s_G(分次强素根),us_G(分次一致强素根)．     

素特征域上广义Witt李超代数的自同构群

设W是素特征域上无限维或有限维广义Witt李超代数.本文利用W的自然滤过不变性和W的底代数的不变维数性质,证明了W的自同构群AutW同构于W的底代数的容许自同构群,还证明了在此群同构之下,AutW的标准正规列恰好对应W的底代数的容许自同构群的标准正规列,并给出AutW若干较为细致的性质.     

关于线性子空间的并集的一个注记

设V是一个线性空间,不考虑V上的数量乘法运算和加法运算满足的交换律,则V构成一个群.给出了一个群V可以写成三个真子群的并集的充分必要条件．     

具有一对零态射的Morita Context 环(Ⅱ)

设(A,B,V,W,ψ,φ)是一个Morita Context,具有一对零态射ψ=0,φ=0,C= (A V W B)是对应的Morita Context环.本文给出了C与A,B,V,W之间关于环的π-正则性、semiclean性、Mophic性和环的Exchgange性、Potent性、GM性的关系.     

关于Aluthge变换的数值域

设A是作用在希耳伯特空间H上的有界线性算子,如果A=V A是算子A的极分解,则定义A~=A 12V A 21和A~(*)=A*21V A*21分别为算子A的Aluthge变换A~和*-Aluthge变换A~(*).记A~和A~(*)的数值域分别为W(A~)和W(A~(*)).证明了W(A~)=W(A~(*)),即肯定了吴提出的一个猜想.     

The Distance-Regular Graphs of Valency Four

Let W be a Coxeter group acting as a matrix group by way of the dual of the geometric representation. Let L be the lattice of intersections of all reflecting hyperplanes associated with the reflections in this representation. We show that L is isomorphic to the lattice consisting of all parabolic subgroups of W. We use this correspondence to find all W for which L is supersolvable. In particular, we show that the only infinite Coxeter group for which L is supersolvable is the infinite dihedral group. Also, we show how this isomorphism gives an embedding of L into the partition lattice whenever W is of type An, Bn or Dn. In addition, we give several results concerning non-broken circuit bases (NBC bases) when W is finite. We show that L is supersolvable if and only if all NBC bases are obtainable by a certain specific combinatorial procedure, and we use the lattice of parabolic subgroups to identify a natural subcollection of the collection of all NBC bases.     

Cancellation law for homoiopy equivalent representations of groups op odd order

We prove that if V and W are real G-modules and G is a group of odd order, then V and W are stably G-homotopy equivalent if and only if they are G-homotopy equivalent.     

长方矩阵加权群逆的迭代法

1引 言与引理 最近,文[1]定义了长方矩阵的一种加权群逆:设A∈Cm×n,W∈Cn×m.称满足下列矩阵方程组的矩阵X∈Cm×n为A的加W权群逆:(W1)AWXWA=A, (W2)XWAWX=X, (W3)AWX=XWA通常记A的加W权群逆为A#W.若A#W存在,则它是唯一的.     

Generalized Schur-concave Functions and Eaton Triples

Motivated by Schur-concavity, we introduce the notion of G -concavity where G is a closed subgroup of the orthogonal group O ( V ) on a finite dimensional real inner product space V . The triple ( V , G , F ) is an Eaton triple if F ² V is a nonempty closed convex cone such that (A1) Gx 7 F is nonempty for each x ε V . (A2) max g ε G ( x,gy ) = ( x,gy ) for all x, y ε F . If W := span F and H := { g | W : g ε G , gW = W } ² O ( W ), and ( W , H , F ) is an Eaton triple, then ( W , H , F ) is called a reduced triple of the Eaton triple ( V , G , F ). In this event, a characterization of the G -concavity in terms of H -concavity is obtained. Some differential characterizations of G -concavity are then given. The results are applied to Lie groups. Various matrix examples are given.     

Cartan型模李超代数W的二阶上同调群H2(W,F)

本文研究了有限维广义Witt李超代数W的二阶上同调群H2(W,F),其中F是一个特征P＞2的代数封闭域.通过计算W到W*的导子,得到H2(W,F)是平凡的.应用此结果,我们可得W的中心扩张是平凡的.     

Von Neumann equivalence and group exactness

We will show that group exactness is a von Neumann equivalence invariant. This result generalizes the previously known fact stating that group exactness is stable under measure equivalence and W*-equivalence.