The Structure of Crossed Product C*-algebras

叉积C*-代数的结构

基本信息

  • 批准号:
    0070776
  • 负责人:
  • 金额:
    $ 9.89万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2000
  • 资助国家:
    美国
  • 起止时间:
    2000-07-01 至 2004-06-30
  • 项目状态:
    已结题

项目摘要

AbstractPhillipsThe Principal Investigator has recently proved that crossed products of compact manifolds by minimal diffeomorphisms can be represented as direct limits of systems of recursive subhomogeneous C*-algebras with no dimension growth. He proposes to attempt to generalize this result, by relaxing the differentiability assumptions (many interesting minimal homeomorphisms are not smooth, or not even on manifolds), and by considering more general groups (such as the real numbers or the direct sum of several copies of the integers). He also proposes to apply the direct limit decomposition, by attempting to prove a classification theorem for such direct limits, and by using the results it implies about K-theory to investigate the connections between dynamics and C*-algebras for interesting minimal homeomorphisms. The Principal Investigator further proposes to use methods of free probability to study isomorphism questions for C*-algebras related to the reduced C*-algebras of free groups.This project concerns the classification of simple C*-algebras. C*-algebras are a fascinating and beautiful part of mathematics in their own right, and moreover they have surprising applications toother parts of mathematics (such as geometry and topology) and even to parts of physics (such as quantum mechanics and statistical mechanics). For these reasons, and others, one wants to identify and describe all C*-algebras. Without some limitations, this task is presently hopeless, and my project focuses on C*-algebras which are "simple" (that is, the usual way of taking them apart into smaller pieces doesn't work), and also "not too large" in several other technical senses. Under these limitations, some classification theorems have been proved. That is, one can identify, label, and describe the objects in certain classes of C*-algebras, sort of like the periodic table of the elements or like the naming of the species of living things. In one particular case ofinterest (the "stably finite" case), the classification results have been proved for simple C*-algebras arising from one particular construction ("direct limits"), but the most interesting source of examples is a different construction ("crossed products"). In a sense, the wrong algebras have been classified. The aim of this project is to show that some algebras of the more interesting kind are actually the same as some of the ones already classified, or are at least close enough that the old classification methods from direct limits might still be applied; and to extend those methods far enough to actually classify the algebras of the more interesting type.
主要研究者最近证明了紧致流形的极小微分同胚交叉积可以表示为递归次齐次C*-代数系统的不增长的直接极限。他建议通过放松可微性假设(许多有趣的极小同胚不光滑,甚至不在流形上),并通过考虑更一般的群(例如实数或整数的几个副本的直和)来尝试推广这一结果。他还建议应用直接极限分解,试图证明这种直接极限的一个分类定理,并利用它蕴含的关于K-理论的结果来研究有趣的极小同胚的动力学和C*-代数之间的联系。主要研究者进一步提出利用自由概率的方法来研究与自由群的约化C*-代数相关的C*-代数的同构问题。C*-代数本身就是数学中一个迷人而美丽的部分,而且它们在数学的其他部分(如几何和拓扑学)甚至物理的部分(如量子力学和统计力学)中都有令人惊讶的应用。由于这些原因和其他原因,人们想要识别和描述所有的C*-代数。如果没有一些限制,这项任务目前是没有希望的,我的项目专注于C*-代数,它们是“简单的”(即,通常将它们分成更小的部分的方法不起作用),而且在其他几个技术意义上也是“不太大”的。在这些限制下,证明了一些分类定理。也就是说,人们可以在某些C*-代数类中识别、标记和描述对象,有点像元素元素周期表,或者像生物物种的命名。在一个感兴趣的特殊情况下(“稳定有限”情况),简单C*-代数的分类结果已被证明是由一个特定结构(“直接极限”)产生的,但最有趣的例子来源是不同的结构(“交叉积”)。在某种意义上,错误的代数被分类了。这个项目的目的是证明一些更有趣类型的代数实际上与一些已经分类的代数相同,或者至少足够接近,以至于来自直接极限的旧分类方法仍然可以应用;并将这些方法扩展到足够远,以实际对更有趣类型的代数进行分类。

项目成果

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Norman Phillips其他文献

141 QUALITY ASSURANCE SCORES FOR PAEDIATRIC TRANSPORT
  • DOI:
    10.1203/00006450-199407000-00141
  • 发表时间:
    1994-07-01
  • 期刊:
  • 影响因子:
    3.100
  • 作者:
    Andrew J Macnab;Norman Phillips;David F Wensley
  • 通讯作者:
    David F Wensley
The dyslexic copes
  • DOI:
    10.1007/bf02653543
  • 发表时间:
    1974-01-01
  • 期刊:
  • 影响因子:
    2.300
  • 作者:
    Norman Phillips;George Bright;Richard Berg;Foster Nowell
  • 通讯作者:
    Foster Nowell
What Makes the Foucault Pendulum Move among the Stars?
  • DOI:
    10.1007/s11191-004-9471-3
  • 发表时间:
    2004-11-01
  • 期刊:
  • 影响因子:
    2.500
  • 作者:
    Norman Phillips
  • 通讯作者:
    Norman Phillips
The Vancouver sedative recovery scale for children: validation and reliability of scoring based on videotaped instruction

Norman Phillips的其他文献

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{{ truncateString('Norman Phillips', 18)}}的其他基金

NSF-BSF: C*-algebras and Dynamics Beyond the Elliott Program
NSF-BSF:艾略特纲领之外的 C* 代数和动力学
  • 批准号:
    2400332
  • 财政年份:
    2024
  • 资助金额:
    $ 9.89万
  • 项目类别:
    Standard Grant
NSF-BSF: Dynamics and Operator Algebras beyond the Elliott Classification Program
NSF-BSF:艾略特分类计划之外的动力学和算子代数
  • 批准号:
    2055771
  • 财政年份:
    2021
  • 资助金额:
    $ 9.89万
  • 项目类别:
    Standard Grant
Structure of crossed products by amenable groups and classification of group actions
按服从群体划分的交叉产品结构和群体行为分类
  • 批准号:
    1501144
  • 财政年份:
    2015
  • 资助金额:
    $ 9.89万
  • 项目类别:
    Continuing Grant
Support for US participants in the 2012 West Coast Operator Algebra Seminar
为 2012 年西海岸算子代数研讨会美国参与者提供支持
  • 批准号:
    1246668
  • 财政年份:
    2012
  • 资助金额:
    $ 9.89万
  • 项目类别:
    Standard Grant
Classification of group actions and structure of transformation group C*-algebras
群作用的分类和变换群C*-代数的结构
  • 批准号:
    1101742
  • 财政年份:
    2011
  • 资助金额:
    $ 9.89万
  • 项目类别:
    Standard Grant
Support for US participants in the 2010 West Coast Operator Algebra Seminar
为 2010 年西海岸算子代数研讨会美国参与者提供支持
  • 批准号:
    1036073
  • 财政年份:
    2010
  • 资助金额:
    $ 9.89万
  • 项目类别:
    Standard Grant
Group actions on C*-algebras and their crossed products
C* 代数及其交叉积的群作用
  • 批准号:
    0701076
  • 财政年份:
    2007
  • 资助金额:
    $ 9.89万
  • 项目类别:
    Continuing Grant
Special Meeting: Fields Operator Algebras Program--International US Participation
特别会议:场算子代数项目--美国国际参与
  • 批准号:
    0649696
  • 财政年份:
    2007
  • 资助金额:
    $ 9.89万
  • 项目类别:
    Standard Grant
The structure of transformation group C*-algebras
变换群C*-代数的结构
  • 批准号:
    0302401
  • 财政年份:
    2003
  • 资助金额:
    $ 9.89万
  • 项目类别:
    Standard Grant
Topological and Related Aspects of the Structure of C* - Algebras
C* 结构的拓扑和相关方面 - 代数
  • 批准号:
    9706850
  • 财政年份:
    1997
  • 资助金额:
    $ 9.89万
  • 项目类别:
    Standard Grant

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ECLIPSE:使用限速粒子电池模拟进行交叉场放电的多尺度建模
  • 批准号:
    2206904
  • 财政年份:
    2022
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    $ 9.89万
  • 项目类别:
    Standard Grant
Simplicity of reduced crossed products of C*-dynamical systems
C* 动力系统简化交叉积的简单性
  • 批准号:
    535032-2019
  • 财政年份:
    2021
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    $ 9.89万
  • 项目类别:
    Alexander Graham Bell Canada Graduate Scholarships - Doctoral
Regularity Properties and K-Theory of Crossed Product Operator Algebras
叉积算子代数的正则性质与K理论
  • 批准号:
    2055736
  • 财政年份:
    2021
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    $ 9.89万
  • 项目类别:
    Standard Grant
Steering Colloids via Two-Dimensional Diffusiophoresis Using Crossed Gradients in Salt Concentrations
使用盐浓度的交叉梯度通过二维扩散电泳控制胶体
  • 批准号:
    EP/V048473/1
  • 财政年份:
    2021
  • 资助金额:
    $ 9.89万
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    Research Grant
Exotic crossed products and the Baum–Connes conjecture (D02)
奇异的交叉积和 BaumâConnes 猜想 (D02)
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    444035660
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    2020
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    $ 9.89万
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    Collaborative Research Centres
Simplicity of reduced crossed products of C*-dynamical systems
C* 动力系统简化交叉积的简单性
  • 批准号:
    535032-2019
  • 财政年份:
    2020
  • 资助金额:
    $ 9.89万
  • 项目类别:
    Postgraduate Scholarships - Doctoral
Crossed reflex pathways and their role during locomotor behavior in mice
交叉反射途径及其在小鼠运动行为中的作用
  • 批准号:
    RGPIN-2015-03871
  • 财政年份:
    2019
  • 资助金额:
    $ 9.89万
  • 项目类别:
    Discovery Grants Program - Individual
Crossed Products of Operator Algebra Dynamical Systems
算子代数动力系统的叉积
  • 批准号:
    504008-2017
  • 财政年份:
    2019
  • 资助金额:
    $ 9.89万
  • 项目类别:
    Alexander Graham Bell Canada Graduate Scholarships - Doctoral
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  • 批准号:
    535032-2019
  • 财政年份:
    2019
  • 资助金额:
    $ 9.89万
  • 项目类别:
    Postgraduate Scholarships - Doctoral
Crossed reflexes in mice
小鼠的交叉反射
  • 批准号:
    541371-2019
  • 财政年份:
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