Study on algebraic・topological・analytic K theory

代数·拓扑·解析K理论研究

基本信息

批准号：
63540081
负责人：
ODA Nobuyuki
金额：
$ 1.02万
依托单位：
Fukuoka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1988
资助国家：
日本
起止时间：
1988 至 1989
项目状态：
已结题

项目摘要

We obtained the following results.1. We determined general results on continuous saps which are honotopic to a fixed map on the finite sketetons.2. We succeeded to generalize the concepts of Gottlieb sets and Varadarajan sets. We studied the actions of the fundamental groups and localizations.3. We obtained some results on the spaces with an indefinite inner-product.4. We obtained a result on a generatization of Tomita-Takesaki theory to a *-algebra.5. We call a family which is closed under a partially defined product a partial O*-algebra, and studied the properties of the algebra. We studied a family of unbounded operators algebraically.6. We studied a projective plane of order 27. We determined a translation complement group by a method of Oyama.7. We also constructed some new translation planes of order 27. Furthermore we obtained a generatization of the Sherk plane of general order.8. We studied the local algebra of homogeneous Banach algebra on 1-dimensioned torus. We determined the structure of type-C to some extent.9. We studied the properties of CCR-algebras. We proved Tomita-Takesaki theorem for a representation which is fundamental for the study.10. We determined a condition for real valued plurisubharmonic function to be the real part of a holomorphic function on a Riemann domain over a flag manifold.11. We obtained a condition for real valued plurisubharmonic function to be the real part of a holomorphic function, using cohomology group.

我们获得了以下结果1。我们确定了对有限sketetons的固定地图的连续SAP的一般结果。2。我们成功地概括了Gottlieb集和Varadarajan集的概念。我们研究了基本群体和本地化的行动3。我们在不确定的内部产品的空间上获得了一些结果。4。我们获得了对tomita-takesaki理论的生成 *-Algebra.5的结果。我们称之为部分定义产品的家庭为部分O* - 代数，并研究了代数的特性。我们通过代数研究了一个无限的运营商家庭。6。我们研究了一个命令27的投影平面。我们通过Oyama的方法确定了一个翻译补体组。7。我们还构建了一些订单27的新翻译平面。此外，我们获得了通用秩序的船长平面8。我们研究了1尺度的圆环的均质Banach代数的当地代数。我们在一定程度上确定了C型的结构9。我们研究了CCR-Elgebras的特性。我们证明了Tomita-Takesaki定理的代表，这对于研究至关重要。10。我们确定了真实有价值的Plurisubharmonic函数的条件是在flag歧管上riemann域上塑形函数的实际部分。11。我们获得了使用共同体学组的实际有价值的Plurisubharmonic函数成为全体形态函数的实际部分的条件。