A-稳定秩下的酉K1-群

A.Bak和唐国平在[1]中引入了Λ-稳定秩条件,这是比过去常用的酉稳定秩条件与绝对稳定秩条件都要弱的新的稳定秩条件.利用这一稳定秩条件证明了酉群(有限生成投射模上二次型的自同构群)的基本子群的正规性、二次型空间的消去性、以及酉K1-群的稳定性.这些结果不仅推广了已有的类似结果、极大地简化了证明过程,而更重要的是降低了稳定秩的下界.     

群似酉系统的膨胀性

本文通过研究群似酉系统的若干重要性质,证明了作用在可分Hilbert空间上的任一群似酉系统都具有膨胀性.这一结果将韩德广与Larson关于群酉系统具有膨胀性的结果扩大到了群似酉系统.     

强π-逆半直积

给出两个半群S和T的半直积是强π-逆半群，强π-E-酉逆半群和E-酉逆半群的充要条件，同时还讨论了E-酉逆半群的最小群同余与半直积的最小群同余之间的关系。     

酉群的热核及应用

本文显式构造出了酉群Ｕ（ｎ），特殊酉群的ＳＵ（ｎ）的热核，作为应用定出了酉群的谱．     

迹稳定秩一的C~*-代数

本文引入了一类迹稳定秩一的C*-代数,证明了迹稳定秩一的C*-代数与AF-代数的张量积是迹稳定秩一的,得到了一个可分的单的有单位元的迹稳定秩一的,并且具有SP性质的C*-代数是稳定秩一的.同时,还讨论了迹稳定秩一的C*-代数的K-群的某些性质.     

交换环上的典型群在一般线性群中的扩群

对任一有1的交换环R, 给出了R上的酉群U_2nR(n≥ 5,含辛群, 正交群和标准酉群) 在R上一般线性群GL_2n R 中扩群的完整刻画.     

单的迹稳定秩一C*-代数的消去性质

本文证明了一个单的有单位元的迹稳定秩一的C*-代数具有消去律,利用此结果证明了单的有单位元的迹稳定秩一的C*-代数是稳定秩一的.最后讨论了迹稳定秩一的C*-代数的K0群的性质.     

Hilbert K-模上酉群的框架表示

本文主要研究了Hilbert K-模上酉群的框架表示的一些基本性质，联系框架的强不相交性，得到了Hilbert K-模上酉群的框架表示的重数是有限的．     

典型群PSU(3,q~2)与2-(v,k,1)设计

讨论自同构群是酉群 PSU(3 ,q2 ) (q=2 l)的区 -本原的 2 -(v,k,1 )设计 .首先证明了它必是点 -本原的 ,然后确定了这种类型的设计 ,即它只能为 2 -(q3+1 ,q+1 ,1 )设计     

有限酉群U_n(F_(q~2))在(s+1,1)型子空间可迁集上的次轨道

本文讨论有限域F_(q~2)上的酉群U_n(F_(q~2))在酉几何V_n(F_(q~2))中的(s+1,1)型子空间可迁集上的次轨道,给出关于轨道数和每个次轨道长的计数公式.     

Darstellung von Hyperebenen in verallgemeinerten affinen Räumen durch Moduln

The starting point of this article is a generalized concept of affine space which includes all affine spaces over unitary modules. Our main result is a representation theorem for hyperplanes of affine spaces: Every hyperplane which satisfies a weak richness condition is induced by a module. ¹     

A stable range for quadratic forms over commutative rings

A commutative ring A has quadratic stable range 1 (qsr(A) = 1) if each primitive binary quadratic form over A represents a unit. It is shown that qsr(A) = 1 implies that every primitive quadratic form over A represents a unit, A has stable range 1 and finitely generated constant rank projectives over A are free. A classification of quadratic forms is provided over Bezout domains with characteristic other than 2, quadratic stable range 1, and a strong approximation property for a certain subset of their maximum spectrum. These domains include rings of holomorphic functions on connected noncompact Riemann surfaces. Examples of localizations of rings of algebraic integers are provided to show that the classical concept of stable range does not behave well in either direction under finite integral extensions and that qsr(A) = 1 does not descend from such extensions.     

On Strongly Stable Normal Operators in Krein Spaces

We give a necessary and sufficient condition for strong stability of bounded normal operators in Krein spaces. A similar result was obtained for unitary operators by M. G. Krein [1], and for selfadjoint operators by H. Langer [2], [3].     

On strongly stable normal operators in Krein spaces

For bounded normal operators in Krein spaces we give a necessary and sufficient condition for strong stability. The same result for unitary operators was obtained by M.G.Krein [1] (see also [2]). For selfadjoint operators we refer to the papers of P.Jonas, H.Langer [3] and H.Langer [4].     

Continuity of magnetic Weyl calculus

We investigate continuity properties of the operators obtained by the magnetic Weyl calculus on nilpotent Lie groups, using modulation spaces associated with unitary representations of certain infinite-dimensional Lie groups.     

The moduli space of stable vector bundles over a real algebraic curve

We study the spaces of stable real and quaternionic vector bundles on a real algebraic curve. The basic relationship is established with unitary representations of an extension of \mathbbZ/2{\mathbb{Z}/2} by the fundamental group. By comparison with the space of real or quaternionic connections, some of the basic topological invariants of these spaces are calculated.     

Amenable unitary representations of locally compact groups

Summary A notion of amenability for an arbitrary unitary group representation is introduced. This unifies and generalizes the notions of amenable homogeneous spaces and of inner-amenable groups. Amenable locally compact groups are characterized by the amenability of all their unitary representations. Amenable representations are characterized by several properties which are operator theoretic analogues of properties characterizing amenable groups. We give a generalization to arbitrary representations of Hulanicki-Reiter theorem. This is used in order to describe the amenable representations of the groups with Kazhdan property (T).     

STABILIZATION OF UNITARY GROUPSOVER POLYNOMIAL RINGS

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p-Adic valued quantization

This review covers an important domain of p-adic mathematical physics — quantum mechanics with p-adic valued wave functions. We start with basic mathematical constructions of this quantum model: Hilbert spaces over quadratic extensions of the field of p-adic numbers ? _p , operators — symmetric, unitary, isometric, one-parameter groups of unitary isometric operators, the p-adic version of Schrödinger’s quantization, representation of canonical commutation relations in Heisenberg andWeyl forms, spectral properties of the operator of p-adic coordinate.We also present postulates of p-adic valued quantization. Here observables as well as probabilities take values in ? _p . A physical interpretation of p-adic quantities is provided through approximation by rational numbers.     

Projective spaces on partially ordered sets and Desargues' postulate

We introduce a generalized concept of projective and Desarguean space where points (and lines) may be of different size. Every unitary module yields an example when we take the 1-and 2-generated submodules as points and lines. In this paper we develop a method of constructing a wide range of projective and Desarguean spaces by means of lattices.