Stably Calabi-Yau algebras and skew group algebras

Let G be a finite group and A be a finite-dimensional selfinjective algebra over an algebraically closed field. Suppose A is a left G-module algebra. Some suficient conditions for the skew group algebra AG to be stably Calabi-Yau are provided, and some new examples of stably Calabi-Yau algebras are given as well.     

互素作用下的不变块(英文)

令A,G为有限群且(|A|,|G|)=1.设A通过自同构作用在G上.令B是G的A-不变块.若B的每一个指标都是A-不变的,且B的亏群是循环群,则A中心化B的某一亏群.     

K-POTENT PRESERVING LINEAR MAPS

Let B(X) be the Banach algebra of all bounded linear operators on a complex Banach space X. Let k ≥ 2 be an integer and φ a weakly continuous linear surjective map from B(X) into itself. It is shown that φ is k-potent preserving if and only if it is k-th-power preserving, and in turn, if and only if it is either an automorphism or an antiautomorphism on B(X) multiplied by a complex number λ satisfying λk-1= 1. Let A be a von Neumann algebra and B be a Banach algebra, it is also shown that a bounded surjective linear map from A onto B is k-potent preserving if and only if it is a Jordan homomorphism multiplied by an invertible element with (k - l)-th power I.     

Auslander Categories and Free Normalizing Extensions

Let RCS be a semidualizing(R,S)-bimodule.Then RCS induces an equiv-alent between the Auslander class AC(S)and the Bass class BC(R).Let A and B be free normalizi...     

On some properties of Segal algebras and their multipliers

Let A and B be Banach algebras such that A is a right abstract Segal algebra in B. We investigate some properties of A and B and show how these are related to the algebras of right multipliers on A and B.     

On the Root-Class Residuality of Certain Free Products of Groups with Normal Amalgamated Subgroups

Russian Mathematics - Let $${\cal K}$$ be a root class of groups closed under taking quotient groups, G be a free product of groups A and B with amalgamated subgroups H and K. Let also H be normal...     

布尔矩阵行空间基数的存在点

设 Ｂｎ 表示所有的ｎ 阶布尔矩阵的集合, Ｒ（ Ａ）表示 Ａ∈ Ｂｎ 的行空间,｜ Ｒ（ Ａ）｜表示 Ｒ（ Ａ）的基数．设ｍ ,ｎ,ｋ 为正整数,本文证明了当ｎ≥９, ｎ＋ ５２ ≤ｋ≤ｎ－ ３ 时,对任意的 ｍ ,２ｋ≤ｍ ≤２ｋ＋ ２ｎ－ ｋ＋ ２＋ ２ｎ－ ｋ＋ １ ＋ …＋ ２３,存在 Ａ∈ Ｂｎ,使得｜ Ｒ（ Ａ）｜＝ ｍ ．     

Residual Separability of Subgroups in Free Products with Amalgamated Subgroup of Finite Index

Siberian Mathematical Journal - Let P be the free product of groups A and B with amalgamated subgroup H, where H is a proper subgroup of finite index in A and B. We assume that the groups A and B...     

On a Conjecture of Kontsevich and Variants of Castelnuovo's Lemma

Let A=(aij) be an orthogonal matrix (over R or C) with no entries zero. Let B= (bij) be the matrix defined by bij= 1/ai j. M. Kontsevich conjectured that the rank of B is never equal to three. We interpret this conjecture geometrically and prove it. The geometric statement can be understood as variants of the Castelnuovo lemma and Brianchon's theorem.     

标准算子代数上保因子交换性的映射

Let X, Y be real or complex Banach spaces with dimension greater than 2 and A, B be standard operator algebras on X and Y, respectively. Let φ ：A →B be a unital surjective map. In this paper, we characterize the map φ on .4 which satisfies （A - B）R = R（A-B） ξR （（A-B）→ （φ（B））φ（R） =φ（R）（（A）- （B）） for A, B, R E .4 and for some scalar     

Noether环上的幂稳定自由模

设I是Noether环R的投射理想, I^m=Iⁿ, m≠n. 该文证明, 有限生成投射右R - 模幂稳定自由当且仅当(1) 存在环S使得I^|m-n|( S ( R且有限生成投射S - 模是幂稳定自由; (2) 有限生成投射右R/I^|m-n| - 模幂稳定自由.     

标准算子代数上的和导子有关的函数方程的Hyers-Ulam-Rassias稳定性

设■是复Hilbert空间,■是■上有界线性算子全体,■是标准算子代数且对于伴随运算封闭.本文结合广义Jensen等式证明了标准算子代数■上的和导子有关的函数方程具有广义Hyers-Ulam-Rassias稳定性.     

幂群与它的生成群

设г是G上的幂群,即以G的非空子集为元素,在G的子集的运算之下所成的群.P_1,P_2是这样的两个性质 P_1:对任意g∈G,存g∈G,存在A∈г,使得g∈A. P_2:对任意A,B∈г,如果A≠B,则A∩B=φ. 本文得出了群G上的幂群г分别具有性质P_1或P_2的充要条件.     

两个四元数自共轭矩阵乘积的特征值估计

设A和B都是四元数自共轭半正定矩阵，或者其中之一是正定的，而另一个是自共轭的，本文改进并推广了[2]对乘积AB的特征值估计.     

A result on direct products of copies of the integers

Let P be the direct product of an infinite number of copies of the integers. If P = A?B as an abelian group, then A or B is isomorphic to P     

ON THE SPECTRAL PROPERTIES OF M-MATRICES AND ITS APPLICATIONS

1.IntroductionAndPreliminariesThespectralpropertiesofM-matricesplayanimportantroleinnonnegativemainstheory,andhavebeenappliedtostudythenumericalsolutionoflinearsystems.Recentlylmanyarticleshavediscussedwiththistopics(see[l--5]).ThepurposeofthispaperistoestablishthespectralinequalitiesofsingularM-matrices.ByapplyingthesepropertiesweanswerpartiallyanopenproblemandsolveanopenproblemposedbySchneiderin[4,5],somerecelltresultI2'4'6]onsplittingsofanM-matrixarealsoimproved.Allnotationsanddefinitio…     

Stably free modules over rings of Laurent polynomials

Let Φ be a finite group and let A be the group algebra of a free abelian group over a field k. We show that, in general, A[Φ] admits nontrivial stably free modules. By contrast, if A is the group algebra of a finitely generated free group then A[Φ] has stably free cancellation.     

Retracts that are kernels of locally nilpotent derivations

Czechoslovak Mathematical Journal - Let k be a field of characteristic zero and B a k-domain. Let R be a retract of B being the kernel of a locally nilpotent derivation of B. We show that if B = R...     

τ-可测正算子生成的交换子的若干不等式

设M是具有正规忠实的半有限迹τ的von Neumann代数,‖.‖ρ是任意非交换Banach函数空间范数,‖.‖是M上的通常范数.证明了若A和B是τ-可测正算子,X∈M,则‖AX-XB‖ρ≤‖X‖‖AB‖ρ.还证明了若A,B是M中的正算子,X是τ-可测算子,则‖AX-XB‖ρ≤max(‖A‖,‖B‖)‖X‖ρ.由此得到了若A∈M是正算子,X是τ-可测正算子,则‖AX-XA‖ρ≤1/2‖A‖‖XX‖ρ.     

Definability of Completely Decomposable Torsion-Free Abelian Groups by Endomorphism Semigroups and Homomorphism Groups

Mathematical Notes - Let C be an Abelian group. A class X of Abelian groups is called a CE?H-class if, for every groups A, B ∈ X, the isomorphisms E?(A) ? E?(B) and...