Topological and Related Aspects of the Structure of C* - Algebras

C* 结构的拓扑和相关方面 - 代数

基本信息

  • 批准号:
    9706850
  • 负责人:
  • 金额:
    $ 8.34万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    1997
  • 资助国家:
    美国
  • 起止时间:
    1997-06-01 至 2000-05-31
  • 项目状态:
    已结题

项目摘要

Abstract Phillips The Principal Investigator, N. Christopher Phillips, proposes three lines of research: (1) work on the classification and structure of simple C*-algebras; (2) a functional analytic characterization of the algebra of smooth functions on a smooth manifold; and (3) a continuation of his previous work on exponential rank. In (1), he proposes to work with Qing Lin on understanding the structure of transformation group C*-algebras of minimal diffeomorphisms. The eventual goal is to show that they are direct limits of sub-homogeneous C*-algebras, which would put them close to the classifiable class of stably finite simple C*-algebras. Several already interesting intermediate results, such as cancellation results in the K-theory of these algebras, are closer to realization. He also proposes to follow up recent work on the purely infinite case of the classification in several ways: a possibility of interesting invariants in the non-nuclear case, a long shot possibility for proving that nuclearity implies the Universal Coefficient Theorem, and a very plausible approach to the real case of the known classification theorem. In (2), he proposes to try to prove a functional analytic characterization of the algebra of smooth functions on a smooth manifold, in an effort to gain a better understanding of what a noncommutative manifold should be. In (3), he proposes to search for a simple C*-algebra with large exponential rank, and to try to understand better the exponential rank of stable and homogeneous C*-algebras. The purpose of this project is to improve the understanding of he "simple" C*-algebras. A C*-algebra is a kind of algebraic system (somewhat like the set of real numbers, with its operations of addition, subtraction, multiplication, and division, but somewhat more complicated). It has additional structure which, roughly speaking, describes when something is "large" or "small" (again, somewhat like the set of real numbers). C*-algebras turn out to be one of the more impor tant kinds of structures in mathematics. They have significant applications to other parts of mathematics which at first sight seem rather unrelated (geometry, for example), and they are also one of the kinds of structure that is important in quantum mechanics, the (rather counterintuitive) physical theory needed to deal properly with atoms and other very small objects. The simple C*-algebras are those that cannot be broken into smaller pieces, and in some sense all C*-algebras are built out of them. The project has two main goals. One is to advance the understanding of the "internal structure" of simple C*-algebras, more or less to know about each one all that it is possible to know. This is relevant when they are used in other subjects. The other is to improve the knowledge of the classification of C*-algebras: one wants a complete list of all of them, with a recipe for deciding when two simple C*-algebras, obtained in different ways, are actually the same.
首席研究员N. Christopher Phillips提出了三个研究方向:(1)研究简单C*-代数的分类和结构;(2)光滑流形上光滑函数代数的泛函解析刻划;(3)继续他之前关于指数秩的研究。在(1)中,他提议与林青一起研究极小微分同态的变换群C*-代数的结构。最终的目标是证明它们是次齐次C*-代数的直接极限,这将使它们接近稳定有限简单C*-代数的可分类类。一些已经很有趣的中间结果,如这些代数的k理论中的消去结果,更接近于实现。他还建议从几个方面对最近关于分类的纯无限情况的工作进行后续研究:在非核情况下有趣的不变量的可能性,证明核意味著普适系数定理的可能性,以及对已知分类定理的真实情况的一种非常合理的方法。在(2)中,他提出尝试证明光滑流形上光滑函数代数的泛函解析表征,以更好地理解非交换流形应该是什么。在(3)中,他提出寻找具有大指数秩的简单C*-代数,并试图更好地理解稳定齐次C*-代数的指数秩。这个项目的目的是提高对“简单”C*-代数的理解。C*代数是一种代数系统(有点像实数的集合,具有加、减、乘、除的运算,但更复杂一些)。它有额外的结构,粗略地说,描述什么时候是“大”或“小”(再一次,有点像实数的集合)。C*代数是数学中最重要的结构之一。它们在数学的其他部分有重要的应用,这些部分乍一看似乎不相关(例如几何),它们也是量子力学中重要的一种结构,量子力学是一种(相当违反直觉的)物理理论,需要适当地处理原子和其他非常小的物体。简单的C*代数是那些不能被分解成小块的代数,在某种意义上,所有的C*代数都是由它们构成的。该项目有两个主要目标。一个是推进对简单C*-代数“内部结构”的理解,或多或少地了解每一个代数,所有可能知道的。当它们用于其他科目时,这是相关的。另一个目的是提高对C*-代数分类的认识:人们想要一个C*-代数的完整列表,并有一个公式来判断两个简单的C*-代数,以不同的方式获得,实际上是相同的。

项目成果

期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ monograph.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ sciAawards.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ conferencePapers.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ patent.updateTime }}

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

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

{{ 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:
    $ 8.34万
  • 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:
    $ 8.34万
  • 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:
    $ 8.34万
  • 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:
    $ 8.34万
  • 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:
    $ 8.34万
  • 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:
    $ 8.34万
  • 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:
    $ 8.34万
  • 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:
    $ 8.34万
  • 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:
    $ 8.34万
  • 项目类别:
    Standard Grant
The Structure of Crossed Product C*-algebras
叉积C*-代数的结构
  • 批准号:
    0070776
  • 财政年份:
    2000
  • 资助金额:
    $ 8.34万
  • 项目类别:
    Continuing Grant

相似国自然基金

Brahma related gene 1/Lamin B1通路在糖尿病肾脏疾病肾小管上皮细胞衰老中的作用
  • 批准号:
  • 批准年份:
    2021
  • 资助金额:
    10.0 万元
  • 项目类别:
    省市级项目
植物RETINOBLASTOMA-RELATED (RBR)蛋白网络调控根尖干细胞损伤修复的分子机制
  • 批准号:
  • 批准年份:
    2020
  • 资助金额:
    58 万元
  • 项目类别:
C1q/TNF-related protein 9调控平滑肌细胞程序性坏死抑制动脉粥样硬化的机制研究
  • 批准号:
    81900309
  • 批准年份:
    2019
  • 资助金额:
    21.0 万元
  • 项目类别:
    青年科学基金项目
降钙素基因相关肽(Calcitonin gene-related peptide, CGRP)对穴位敏化的调节及机制研究
  • 批准号:
    81873385
  • 批准年份:
    2018
  • 资助金额:
    59.0 万元
  • 项目类别:
    面上项目
C1q/TNF-related protein-3在银屑病代谢紊乱中的作用及机制研究
  • 批准号:
    81402620
  • 批准年份:
    2014
  • 资助金额:
    23.0 万元
  • 项目类别:
    青年科学基金项目

相似海外基金

New aspects of kimberlite-related metasomatism
与金伯利岩相关的交代作用的新方面
  • 批准号:
    RGPIN-2019-03988
  • 财政年份:
    2022
  • 资助金额:
    $ 8.34万
  • 项目类别:
    Discovery Grants Program - Individual
Diet and foraging-related aspects of host-parasite dynamics in freshwater systems
淡水系统中宿主-寄生虫动态的饮食和觅食相关方面
  • 批准号:
    RGPIN-2020-04622
  • 财政年份:
    2022
  • 资助金额:
    $ 8.34万
  • 项目类别:
    Discovery Grants Program - Individual
New aspects of kimberlite-related metasomatism
与金伯利岩相关的交代作用的新方面
  • 批准号:
    RGPIN-2019-03988
  • 财政年份:
    2021
  • 资助金额:
    $ 8.34万
  • 项目类别:
    Discovery Grants Program - Individual
Diet and foraging-related aspects of host-parasite dynamics in freshwater systems
淡水系统中宿主-寄生虫动态的饮食和觅食相关方面
  • 批准号:
    RGPIN-2020-04622
  • 财政年份:
    2021
  • 资助金额:
    $ 8.34万
  • 项目类别:
    Discovery Grants Program - Individual
Diet and foraging-related aspects of host-parasite dynamics in freshwater systems
淡水系统中宿主-寄生虫动态的饮食和觅食相关方面
  • 批准号:
    RGPIN-2020-04622
  • 财政年份:
    2020
  • 资助金额:
    $ 8.34万
  • 项目类别:
    Discovery Grants Program - Individual
New aspects of kimberlite-related metasomatism
与金伯利岩相关的交代作用的新方面
  • 批准号:
    RGPIN-2019-03988
  • 财政年份:
    2020
  • 资助金额:
    $ 8.34万
  • 项目类别:
    Discovery Grants Program - Individual
Multi-aspects of beta ensembles and related random matrix models
β 系综和相关随机矩阵模型的多方面
  • 批准号:
    19K14547
  • 财政年份:
    2019
  • 资助金额:
    $ 8.34万
  • 项目类别:
    Grant-in-Aid for Early-Career Scientists
New aspects of kimberlite-related metasomatism
与金伯利岩相关的交代作用的新方面
  • 批准号:
    RGPIN-2019-03988
  • 财政年份:
    2019
  • 资助金额:
    $ 8.34万
  • 项目类别:
    Discovery Grants Program - Individual
Multi-state, multi-time, multi-level analysis of health-related demographic events: Statistical aspects and applications
健康相关人口事件的多状态、多时间、多层次分析:统计方面和应用
  • 批准号:
    386913674
  • 财政年份:
    2017
  • 资助金额:
    $ 8.34万
  • 项目类别:
    Research Grants
Computational aspects of queueing and related problems
排队的计算方面及相关问题
  • 批准号:
    481157-2015
  • 财政年份:
    2015
  • 资助金额:
    $ 8.34万
  • 项目类别:
    University Undergraduate Student Research Awards
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了