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

K-Theory, C*-algebras and Index theory

K-理论、C*-代数和指数理论

基本信息

批准号：
33974342
负责人：
Professor Dr. Michael Frank
金额：
--
依托单位：
Fakultät Informatik und Medien
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2006
资助国家：
德国
起止时间：
2005-12-31 至 2009-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/33974342?language=en
关键词：
Theory algebras Index theory

项目摘要

In this proposed German-Russian research cooperation, the focus lies in K-theory of C*-algebras and related topics. This ranges from twisted K-theory where recent interest stems from its proposed applications in string theory and mathematic physics over approaches to the K-theory of C*-algebras via almost flat bundles and via Burnside theory and asymptotic homomorphism, it also covers the application of K-theoretic methods to the study of boundary value problems. The methods of modern approaches to the K-theory of C*-algebras carry much further, and can be used to gain important insights into the structure of C*-algebras, and much more generally to understand new aspects of noncommutative geometry, topology, and probability theory. The central object here are Hilbert C*-modules; which will be a focus of research for approaches to conditional expectations and frames in non-commutative probability theory. The global analysis parts of these areas are extended to the study of dynamical Lefschetz formulas, thus providing a bridge to number theory. The principal investigators from Germany and Moscow have build up a large body of experience in the proposed fields; which is in many cases complementary. To make further progress, we now plan to build intensive links (and strengthen the existing ones) between the different groups in Germany and Moscow. During the project, further progress shall be made in the conceptual understanding of the underlying principles and in explicit computational results and application. For this, an intense exchange program for the participating researchers from Moscow and Germany is necessary. Funding for this exchange is the main aim of the present proposal.

在这次提出的德俄研究合作中，重点在于C*-代数的K-理论及相关课题。这范围从扭曲的K-理论，最近的兴趣源于其提出的应用在弦理论和数学物理的方法，以K理论的C*-代数通过几乎平坦的丛，并通过伯恩赛德理论和渐近同态，它也涵盖了应用K-理论的方法研究边值问题。C*-代数的K-理论的现代方法进行得更远，并可用于获得对C*-代数结构的重要见解，以及更广泛地理解非交换几何，拓扑学和概率论的新方面。这里的中心对象是希尔伯特C*-模;这将是非交换概率论中条件期望和框架方法的研究重点。这些领域的整体分析部分扩展到研究动态Lefschetz公式，从而提供了一个桥梁数论。来自德国和莫斯科的主要研究人员在拟议领域积累了大量经验;在许多情况下，这些经验是互补的。为了取得进一步的进展，我们现在计划在德国和莫斯科的不同团体之间建立密切的联系（并加强现有的联系）。在项目期间，将在对基本原理的概念理解以及明确的计算结果和应用方面取得进一步进展。为此，来自莫斯科和德国的参与研究人员的密集交流计划是必要的。本提案的主要目的是为这一交流提供资金。