Research for Hilbert C^-bimodules and associated C^-algebras

Hilbert C^*-双模及相关 C^*-代数研究

基本信息

批准号：
09640189
负责人：
KAJIWARA Tsuyoshi
金额：
$ 1.6万
依托单位：
Okayama University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640189/
关键词：
Hilbert bimodule Crossed product dynamical system Simplicity Hilbert bimodule C^*-algebra crossed product

项目摘要

1. We define crossed product C*-bimodule by finite group, and obtain some fundamental results. More-over, we study A-D duality in operator algebra theory by this method. These results are published in "Crossed products of Hilbert *C-bimodules by countable discrete groups".2. We define crossed product C*-bimodule by bundles over finite groups, and prove the associativity law for multiple crossed products. These results are published in "Crossed products of Hilbert C*-bimodule by bundles.3. We investigate ideal structures of C*-algebras associated with finitely generated Hilbert C*-bimodules over unital C*-algebras A.We define the condition (I) and show the simplicity under this condition. Moreover we define the condition (11) and under this condition we present the correspondence the ideals in the bimodules algebras and the ideals of A.We present some examples satisfying these conditions. These results are published in "Ideal structure and simplicity of the C*-algebra generated b9Hilbert bimodules".4. We define coaction on finitely generated Hilbert C*-bimodule by finite groups. We show that resulting crossed product is made into a finitely generated Hilbert C*-bimodule. This results is published in "Coaction crossed products of Hubert C*-bimodule by finite groups".5. We define Hilbert C*-bimodules for countable continuous graphs whose components are 1-dimensional torus, and study the structure of associated C*-algebras. We obtain simplicity and ideal structure of these algebras. These results are published in "Hilbert C*-bimodules and countably infinite continuous graphs"6. We are studying singular dynamical system using Hilbert C*-bimodule method. We construct natural basis for the bimodule associated with the tent map. We are plan to. define conjugacy invariant for the above dynamical systems using our method.

1。我们通过有限组定义了交叉产品C*-Bimodule，并获得一些基本结果。越来越多，我们通过这种方法研究了操作员代数理论中的A-D双重性。这些结果发表在“由可数离散组的Hilbert *C-Bimodules的交叉产品中” .2。我们通过有限基团的束定义交叉产品c*bimodule，并证明了多种跨产品的关联定律。这些结果发表在捆绑包中的“希尔伯特C*bimodule的交叉产物中。3。我们研究了与unitial c*-Algebras上有限生成的Hilbert C*-bimodules相关的C* - 代数的理想结构。 A.我们的理想是满足这些结果的一些例子。 “有限基团的co跨产物跨越了bimodule”。5我们定义了Hilbert C*-Bimodules，用于可计数的连续图，其组件是1维圆环，并研究了相关的C*-ergebras的结构。我们获得这些代数的简单性和理想结构。这些结果发表在“ Hilbert C*Bimodules和次数无限连续图”中6。我们正在使用Hilbert C*-Bimodule方法研究奇异的动力系统。我们为与帐篷图关联的双模型构建自然基础。我们计划。使用我们的方法为上述动态系统定义共轭不变。