EQUIVARIANT COHOMOLOGY AND REPRESENTATIONS OF THE SYMMETRIC GROUP

51. IntroductionIn a recent paper [l], I have shown how to construct a continuous mapf: Cn(R') - U(n)/T"from the configuration space of n ordered distinct points of R3 to the flag manifold of U(n)which is compatible with the natural action of the symmetric group Z. on both spaces. Ialso noted in [1] that the action of E. on the rational cohomology of either space coincideswith the regular representation but that the homomorphism f* induced by f cannot possiblybe an isomorphism. In fact the…     

HX环的存在性

自李洪兴１９９１年提出了ＨＸ环这一问题以来,一直有这么一个问题没有解决,即是否存在非平凡的ＨＸ环的例子？但至今既没有找到非平凡的ＨＸ环,也没有证明任一环Ｒ上仅存在平凡的ＨＸ环,钟育彬１９９５年证明了一类环上仅存在平凡的ＨＸ环,那么,是否所有环仅存在平凡的ＨＸ环呢？针对这一点,本文作进上步研究,构造了一个非平凡的ＨＸ环,并建立了ＨＸ环上的同态与同构定理,为进上步研究ＨＸ环奠定了基础。     

THE FUNDAMENTAL GROUP OFTHE AUTOMORPHISM GROUP OFA NONCOMMUTATIVE TORUSTHE FUNDAMENTAL GROUP OFTHE AUTOMORPHISM GROUP OFA NONCOMMUTATIVE TORU

1. IntroductionGiven a locally compact abelian group G and a multiplier p on G, one can associate tothem the twisted group C*-algebra C*(G, p), which is the universal object for unitary prepresentations of G. C* (Zm, p) is said to be a noncommutative torns of rank m and denotedby A.. The multiplier p determines a subgroup S. of G, called its symmetry group, andthe multiplier p is called totally skew if the symmetry group S. is trivial. And A. is calledcompletely irrational if p is totally…     

关于无穷线性方程组的相容性

本文研究无穷线性方程组的相容性，采用的方法是Abel群同态的延拓．     

THE FUNDAMENTAL GROUP OF THE AUTOMORPHISM GROUP OF A NONCOMMUTATIVE TORUS

Assume that each completely irrational noncommutative torus is realized as an inductive limit of circle algebras, and that for a completely irrational noncommutative torus Aw of rank m there are a completely irrational noncommutative torus Aρ of rank m and a positive integer d such that tr(Aw)=1/d.tr(Aρ).It is proved that the set of all C^*-algebras of sections of locally trivial C^*-algebra bundles over S^2 with fibres Aω has a group sturcture,denoted by π1^s(Aut(Aω)),which is isomorphic to Zif Ed>1 and {0} if d>1.Let Bcd be a cd-homogeneous C^*-algebra over S^2×T^2 of which no non-trivial matrix algebra can be factored out.The spherical noncommutative torus Sρ^cd is defined by twisting C^*(T2×Z^m-2) in Bcd ×C^*(Z^m-3) by a totally skew multiplier ρ on T^2×Z^m-2。It is shown that Sρ^cd×Mρ∞ is isomorphic to C(S^2)×C^*(T^2×Z^m-2,ρ）× Mcd(C)×Mρ∞ if and only if the set of prime factors of cd is a subset of the set of prime factors of p.     

直觉模糊正规子群与直觉模糊商群

在直觉模糊子群的基础上 ,引入直觉模糊正规子群与直觉模糊商群概念 ,并讨论了它们的一些性质 ,最后研究了群同态下 ,直觉模糊正规子群的对应关系     

ON THE HARISH－CHANDRA HOMOMORPHISM FOR THE CHEVALLEY GROUPS OVER P－ADIC FIELD

ＯＮＴＨＥＨＡＲＩＳＨ－ＣＨＡＮＤＲＡＨＯＭＯＭＯＲＰＨＩＳＭＦＯＲＴＨＥＣＨＥＶＡＬＬＥＹＧＲＯＵＰＳＯＶＥＲＰ－ＡＤＩＣＦＩＥＬＤ￥ＣＨＥＮＺＨＯＮＧＨＵ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉａｎｇｔａｎＵｎｉｖｅｒｓｉｔｙｔＸｉ...     

基于格半群的有限状态自动机的同态

本文研究了格值有限状态自动机(LFSA)的同态和强同态及其性质.利用强同态概念,在格值有限状态自动机的状态集上建立了一种等价关系,得到了格值有限状态自动机的商自动机,证明了商自动机与强同态像自动机同构.     

STML(C)范畴

本文讨论由Lsmooth拓扑分子格和(L1,L2)smooth连续的广义序同态所构成的STML(C)范畴的若干结果,利用集合套的方法给出了态射的若干性质,证明了范畴STML(C)是拓扑范畴.     

GENERALIZATION OF THE NOTION OF FUNDAMENTAL GROUP

The classical definition of fundamental group for a topological space is based on the pathwise connectedness. A space with less path will not be able to be described effectively by its fundamental group. The author introduces a definition of generalized fundamental group for a given topological space by means of its own connectedness. For a well-behaved space, e.g., a locally pathwise and semilocally simply connected compact metric space, the generalized fundamental group coincides with the classical one.     

ISOLATED POINTS OF THE APPROXIMATE POINT SPECTRUM OF CERTAIN LATTICE HOMOMORPHISMS ON Co (X)

Abstract

Suppose X is a locally compact Hausdorff space and C (X) the apace of all continuous complex valued functions on X which vanish at infinity. Let T be a (complex) linear lattice homomorphism on C_o (X) whose adjoint is also a lattice homomorphism. It is sham that every non-zero isolated point of the approximate point spectrum of T lies in the point spectrum of T. An example is given to show that the exclusion of zero is necessary, even when X is compact. The same techniques are then used to show that if also the spectrum of T is finite then T can be written, in a natural manner, as a direct sum of two such lattice homomorphisms; one being an n'th root of an invertible multiplication operator and the other quasi-nilpotent.     

单形和3维立方体乘积上小覆盖的等变协边类的个数

本文研究了小覆盖的等变协边分类.利用示性函数和Stong同态确定了单形和3维立方体乘积上小覆盖的等变协边类的个数,推广了现有文献中的相关结果.     

单形和3维立方体乘积上小覆盖的等变协边类的个数

本文研究了小覆盖的等变协边分类. 利用示性函数和Stong同态确定了单形和3维立方体乘积上小覆盖的等变协边类的个数, 推广了现有文献中的相关结果.     

整系数射影么模羣的自同构

<正> §1.序言 以表行列式之值为±1的n×n整系数矩陣所組成的乘法羣,而以表中行列式之值为+1的矩陣所組成的子羣.的中核由{I,-I}所組成(I是单位矩阵).以表对其中核的商羣,称之为的射影羣.当n是偶数吋,的中核也是由{I,-I}所組成,以表对其中核之商羣,称之为整系数射影模羣. 华罗庚教授和I.Reiner在[1]中决定了,及(m≥1)的自同构.当n是奇     

THE ACTION OF THE LINEAR CHARACTER GROUP ON THE SET OF NON-LINEAR IRREDUCIBLE CHARACTERS THE ACTION OF THE LINEAR CHARACTER GROUP ON THE SET OF NON-LINEAR IRREDUCIBLE CHARACTERS

1. Notations and Basic ResultsLet G be a finite nonabelian group. Then frs(G/G') is an abelian group under themultiplication of characters and acts on the set of non-linear irreducible characters of G viathe multiplication of characters. The purpose of this paper is to investigate this action. Asan application of our theoryl in the end of Section 3 we give the classification of groupshaving exactly three non-linear irreducible caracters.All groups in the paper are finite. For a factor grou…     

Heisenberg群上Laplace算子的离散谱

本文证明了Heisenberg群上Laplace算子的Dirichlet特征值的存在性，给出了特征值的估计     

有限群的Brauer特征标覆盖数

本文研究了有限群G的Brauer特征标覆盖数δ(G)问题.利用常特征标和Brauer特征标上的方法,获得了δ(G)是有限的当且仅当G/Op(G)是非交换单群这个结果,并进一步得到了当δ(G)有限时δ(G)的范围.     

DECIMAL EXTENSIONS OF THE ADDITIVE GROUP OF INTEGERS

We introduce the concept of decimal extension of the additive group of integers. We characterize these extensions as the linearly ordered abelian groups containing at least one Archimedean element. Finally, we study the additive group of rationals and its subgroups as particular cases of decimal extension.