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.我们用有限群定义了叉积C*-双模，并得到了一些基本结果。此外，我们还用这种方法研究了算子代数理论中的A-D对偶性。这些结果发表在“Crossed products of Hilbert *C-bimodules by countable discrete groups”中。 2．我们通过有限群上的丛定义了交叉积C*-bimodule，并证明了多个交叉积的结合律。这些结果发表在“Hilbert C*-双模的丛的交叉积”中。3。我们研究了与单位 C*-代数 A 上有限生成的希尔伯特 C*-双模相关的 C*-代数的理想结构。我们定义了条件 ( I) 并证明了该条件下的简单性。此外，我们定义了条件 (11)，并在该条件下给出了双模代数中的理想与 A 的理想的对应关系。一些满足这些条件的例子发表在“C*-代数生成的b9Hilbert双模的理想结构和简单性”中。4.我们通过有限群定义了有限生成的Hilbert C*-双模上的相互作用。被制成有限生成的 Hilbert C*-bimodule，该结果发表在“Coaction crossed products of Hubert C*-bimodule by Finite groups”中。 5. 我们定义了 Hilbert C*-bimodule。对于其组件是一维环面的可数连续图，并研究相关的 C* 代数的结构。我们获得了这些代数的简单性和理想的结构。这些结果发表在“Hilbert C*-双模和可数无限连续图”6 中。我们正在使用 Hilbert C*-双模方法研究奇异动力系统。我们为与帐篷地图相关的双模块构建了自然基础。我们计划这样做。使用我们的方法定义上述动力系统的共轭不变量。