Characterizations of Centralizable Mappings on Algebras of Locally Measurable Operators

A linear mapping φ from an algebra A into its bimodule M is called a centralizable mapping at G ∈ A if φ(AB)=φ(A)B=Aφ(B) for each A and B in A with AB=G. In this paper, we prove that if M is a von Neumann algebra without direct summands of type I₁ and type II, A is a *-subalgebra with M ⊆ A ⊆ LS(M) and G is a fixed element in A, then every continuous (with respect to the local measure topology t(M)) centralizable mapping at G from A into M is a centralizer.     

Representation theory of the system quiver

Let A be a three-point algebra with Gabriel quiver the system quiver Q, Then, up to isomorphism and duality, A is tame if and only if A is or degenerates to a factor of a tame algebra in the tame Table T if and only if A/rad5 A is tame, and A is wild if and only if A has a wild algebra in the wild Table W as a factor if and only if A is controlled wild.     

Hopf代数的半单扩张与不变子环的同调维数

设H是域k上的有限维Hopf代数,A是左H-模代数,AH是A的H-不变子环.假定A/AH是半单扩张且A是平坦的右AH-模.如果H*是unimodular,且存在c∈C(A),使t·c=1.我们证明了WD(AH)=WD(A)=WD(A#H).此外,如果A是投射的左及右AH-模,则有LD(AH)=LD(A)=LD(A#H).     

四元数自共轭矩阵乘积的相似变换

本文证明了下列结果:(i)四元数矩阵A可写成两个自共轭四元数矩阵的乘积A相似于实矩阵A Hermite相似于A~*.(ii)A可写成一个半正定自共轭四元数矩阵与一个自共轭四元数矩阵的乘积A相似于实对角矩阵或者A～diag(D,I_r(×)J_2(O)),其中D是一个实对角矩阵.本文还给出了体上实矩阵AB与BA相似的一个充要条件.     

符号空间有限型子转移混沌集的Hausdorff测度与Parry测度

设A是一个每列至少有二个元素为1的不可约0，1方阵，(∑4，σA)为由A所决定的符号空间有限型子转移．在∑A上定义一个与其拓扑相容的度量d使得(∑A，d)的Hausdorff维数为1．若G是H^-可测的σA的Li—Yorke混沌集，则H^1(C)＝0；若A是本原的，则存在一个σA的有限型混沌集S使得H^1(S)＝1，其中H^1为1-维的Hausdorff测度．     

仿射型李代数g(A)的某些自同构群

§0 引言 A=(α_(ij))是n阶广义Cantan矩阵,即A满足:ⅰ)α_(ii)=2,i=1,…n。ⅱ)当i≠j时,α_(ij)是非正整数。ⅲ) a_(ij)=0 α_(ji)=0。 h是复数域C上2n-l维向量空间,h是h的对偶空间。Π={α_1,…α_n},Π分别是h与h中线性无关子集,满足     

一个Lie代数的子代数及其相关的两类Loop代数

本文构造了Lie代数A2的一个子代数A2,通过选取恰当的基元阶数得到相应的一个loop代数A2,由此设计一个等谱问题,利用屠格式得到了一个新的Liouville可积的Hamilton方程族.作为其约化情形,得到了一个非线性有理分式型演化方程.再由一个矩阵变换,得到了换位运算与A2等价的Lie代数A1的一个子代数A1,将A1再扩展成一个新的高维loop代数G,利用G获得了所得方程族的一类扩展可积系统.     

中心化子的刻画

令X为实或复域F上的Banach空间,■为X上的标准算子代数,I是■的单位元.设Φ:■→■是可加映射.本文证明了,如果有正整数m,n,使得Φ满足条件Φ(A~(m+n+1))-A~mΦ(A)A~n∈FI对任意A成立,则存在λ∈F,使得对所有的A∈■,都有Φ(A)=λA.同样的结果对于自伴算子空间上的可加映射也成立.此外,本文还给出了中心素代数上满足条件(m+n)Φ(AB)-mAΦ(B)-nΦ(A)B∈FI的可加映射Φ的完全刻画.     

完全分配格代数中秩一子代数的弱稠密性和套代数的一个特征

如果　Ａ是　Ｈｉｌｂｅｒｔ　空间上的完全分配格代数，　　那么Ａ中秩一算子生成的子代数在　Ａ中弱稠密，　当且仅当，Ａ在迹尖算子空间中的一次和二次预零化子的弱闭包是自反的；如果Ａ是套代数，那么ＬａｔＡ是极大套，当且仅当，Ａ的包含Ａ－的每个弱闭子空间是自反的，其中     

p-亚正常算子的本质谱与拟相似

本文证明了每一个ｐ－亚正常算子Ａ,都相应存在一个亚正常算子 ,使得Ａ与 有相同的闭值域点、相同的本质谱和谱．由此推出如果Ａ是ｐ－亚正常算子,Ｂ是任一有界线性算子,若存在有界线性算子Ｘ有稠值域,使得ＸＢ＝ＡＸ,则σ（Ａ）（Ｂ）此外还证明了,如果Ａ是ｐ－亚正常算子且 Ｒ（Ａ）闭或ＫｅｒＡ＝ＫｅｒＡ*, Ｂ是任一有界线性算子,Ａ与Ｂ拟相似,则ｅ（Ａ）（Ｂ）．     

关于圈的完全正矩阵实现

本文给出了一个关联图为圈的非负、半正定矩阵A为完全正的一个充要条件.我们还证明了这样的矩阵A（当A为完全正时）的分解指数即为A的阶数.     

Banach空间上有界可逆线性变换逆变换的结构

Fillmore在[1]中得到一个定理:设A,T是Banach空间X上的线性变换,A有界,若Lat(A) Lat(T)且AT=TA,则T是A的多项式.在本文里,以此作为引理,讨论了Banach空间上可逆线性变换A在什么情况下,A-1可表示为A的多项式.本文最主要的结论是定理3.4:设X是Banach空间,A是X上的有界线性变换,且可逆,则A-1是A的多项式当且仅当A-1是A的局部多项式.     

Derivations of generalized Weyl algebras

A class of the associative and Lie algebras A[D] = A F[D] of Weyl type are studied, where A is a commutative associative algebra with an identity element over a field F of characteristic zero, and F[D] is the polynomial algebra of a finite dimensional commutative subalgebra of locally finite derivations of A such that A is D-simple. The derivations of these associative and Lie algebras are precisely determined.     

Digraphs and Inclusion Intervals of Brualdi-type for Singular Values

A complex matrix A is said to be a matrix realization of the digraph D if D is the associated digraph of A, and A is said to have the property B if every singular value of A is contained in the union of Brualdi-type intervals. A digraph D is said to be a forcible B-digraph if every matrix realization of D has the property B. In this paper, we give a sufficient condition for a matrix to have the property B and characterize the forcible B-digraphs.     

图的光滑支架分解

设G是一个图,A为其边集的子集。G的一个支架分解是（G－A,A）,其中G－A是去掉A后的连通图,G的一个光滑支架分解是适合下列条件的支架分解：（1）G－A的每一叶具有连通余树;（2）G－B（G－A）割边集为A,其中B（G－A）为G－A的割边集。本文给出了求一个图的光辉支架分解的一个有效算法。     

Lyapunov numbers of markov solutions of linear stochastic systems

All nontrivial solutions of x = A(t)x grow exponentially with rate X(x,w)e{A1,...,Xr}, A a (strictly) stationary matrix process. Projecting x to the unit sphere one obtains for each of the Lyapunov exponents Xt a solution xt with stationary angle st. Now if A is a Markov process one can restrict oneself to Markov solutions, i.e., (x, A) shall be a (joint) Markov process (wich is a restriction on the inital conditions). We prove that whenever there is a Markov solution x with Lyapunov number X then there is another Markov solution with a stationary angle (or equivalently: an invariant measure for the transition probabilities of (s, A)) with the same Lyapunov number. This has some consequences, e.g., for the uniqueness of the Lyapunov numbers     

极大前缀码的一些性质

设X+(X~*)是由字母表X生成的自由(幺)半群且A是X~*的非空子集,如果A∩AX+=φ,则称A是前缀码.如果前缀码A满足:对任意ω∈X+\A,有A∪{ω}不是前缀码,则称A是极大前缀码.给出了极大前缀码的一些性质,并推广了相关文献的结果.     

The influence of X-semipermutability of subgroups on the structure of finite groups

Let A be a subgroup of a group G and X be a nonempty subset of G. A is said to be X-semipermutable in G if A has a supplement T in G such that A is X-permutable with every subgroup of T. In this paper, we investigate further the influence of X-semipermutability of some subgroups on the structure of finite groups. Some new criteria for a group G to be supersoluble or p-nilpotent are obtained.     

Strong conjugation actions induced by flags of exact Borel subalgebras

Let A be a quasi-hereditary algebra with a strong exact Borel subalgebra. It is proved that for any standard semisimple subalgebra T there exists an exact Borel subalgebra B of A such that T is a maximal semisimple subalgebra of B. It is shown that the maximal length of flags of exact Borel subalgebras of A is the difference of the radium and the rank of Grothendic group of A plus 2. The number of conjugation-classes of exact Borel subalgebras is 1 if and only if A is basic; the number is 2 if and only if A is semisimple. For all other cases, this number is 0 or no less than 3. Furthermore, it is shown that all the exact Borel subalgebras are idempotent-conjugate to each other, that is, for any exact Borel subalgebras B and C of A, there exists an idempotent e of A, and an invertible element u of A, such that eBe = u^-1eCeu.     

Classification of Special Anosov Endomorphisms of Nil-manifolds

In this paper we give a classification of special endomorphisms of nil-manifolds:Let f:N/Γ → N/Γ be a covering map of a nil-manifold and denote by A:N/Γ → N/Γ the nil-endomorphism which is homotopic to f. If f is a special T A-map, then A is a hyperbolic nil-endomorphism and f is topologically conjugate to A.