权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Research for Hilbert C*-bimodules and its application to analysis of discrete dynamical systems

Hilbert C*-双模研究及其在离散动力系统分析中的应用

基本信息

批准号：
15540207
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：
2003
资助国家：
日本
起止时间：
2003 至 2006
项目状态：
已结题

项目摘要

1. We proved that the fact a countably generated Hilbert C^*-bimodule if of finite index and the fact that it has a conjugation is equivalent. Moreover, we constructed many examples of countably generated Hilbert C^*-bimodules of finite index. We clarified some properties of bases of Hilbert C^*-modules. These results has been published in "Jones index theory for Hilbert C^*-bimodules and its equivalence with conjugation theory".2. We constructed Hilbert C^*-bimodules from the dynamical systems on the Riemannian sphere given by rational functions, and constructed C^*-algebras using Pimsner construction. We proved simplicity and pure infiniteness of these C^*-algebras. We calculated K-groups for some examples. These results has been published in "C^*-algebras associated with complex dynamical systems".3. We constructed Hilbert C^*-bimodules from self-similar sets given by families of proper contractions, and constructed C^*-algebras using Pimsner construction. Under appropriate conditio … More n, we proved simplicity and pure infiniteness of theseC^*-algebras. We showed that two C^*-algebras differently constructed for SierPinski Gasket, which is a typical fractal, are different using K-group. We also calculated K-group of the C^*-algebra constructed from Koch curve, which is also a typical example. These results has been published in "C^*-algebras associated with self-similar sets".4. We constructed countable basis explicitly for the Hilbert C^*-modules constructed from complex dynamical system and self-similar sets. This construction is a generalization of that given for the Hilbert C^*-module constructed from tent map using the idea of wavelet basis. This seems the first explicit example of countable bases. Although this construction is not contained in the papers which is already published, it gives some help for research of KMS states of C^*-algebras constructed from rational functions and self-similar sets. This research continues in the next period.5. We constructed C^*-algebras for transcendental functions and studied them. We showed simplicity for exponential map case. But there exist a difficulty arising from the existence of pure singularity, and this research also continues. Less

1. 证明了有限指数的可数生成希尔伯特C^*-双模的事实与共轭的事实是等价的。此外，我们构造了许多有限指数的可数生成Hilbert C^*-双模的例子。阐明了Hilbert C^*模的基的一些性质。这些结果发表在《Hilbert C^*-双模的Jones指标理论及其与共轭理论的等价性》。利用有理函数给出的黎曼球上的动力系统构造了Hilbert C^*-双模，并利用Pimsner构造构造了C^*-代数。我们证明了这些C^*-代数的简单性和纯无穷性。我们对一些例子计算了k群。这些结果发表在“C^*-代数与复杂动力系统的关联”。从固有压缩族给出的自相似集构造Hilbert C^*-双模，并利用Pimsner构造构造C^*-代数。在适当的条件下，我们证明了ec ^*-代数的简单性和纯无穷性。我们利用k群证明了SierPinski垫片（SierPinski Gasket）的两个不同构造的C^*-代数是不同的，它是一个典型的分形。我们还计算了由Koch曲线构造的C^*-代数的k群，这也是一个典型的例子。这些结果已发表在“C^*-代数与自相似集相关联”。对于由复动力系统和自相似集构造的Hilbert C^*模，我们显式构造了可数基。这种构造是对Hilbert C^*模的推广，该模是用小波基的思想从帐篷映射构造的。这似乎是可数基数的第一个明确例子。虽然这一构造在已发表的论文中未见，但它对有理函数和自相似集构造的C^*-代数的KMS态的研究有一定的帮助。这项研究将在下一阶段继续进行。构造了超越函数的C^*-代数，并对其进行了研究。我们证明了指数映射情况的简单性。但由于纯奇点的存在，存在着一个困难，这方面的研究还在继续。少