Studies in Operator Algebras

算子代数研究

基本信息

  • 批准号:
    0401043
  • 负责人:
  • 金额:
    $ 15万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2004
  • 资助国家:
    美国
  • 起止时间:
    2004-07-01 至 2008-06-30
  • 项目状态:
    已结题

项目摘要

The proposer will continue his study of the longstanding Kadison--Ringroseconjecture on the cohomology of von Neumann algebras. He will use and refine some recently developed techniques needed to show the complete boundedness of certain multilinear operators. Investigations of the cohomologygroups have led naturally to the recently introduced concept of norming subalgebras, and this topic will be pursued since it applies directly to both cohomology and the bounded projection problem. In a different, but related, direction, maximal abelian subalgebras (masas) and general subalgebras of von Neumann algebras will be studied. In joint work, the proposer has introduced the concept of strongly singular masas, and has shown that many finite factors arising from hyperbolic groups (a class which includes the free groups) have such masas. The results so far obtained indicate that the theory can now expand to study general subalgebras. This relates directly to the structure of factors (the building blocks of operator algebras), and the overall goal of these proposed areas of research is to increase our understanding in this area. Building on previously accomplished work, problems in the theory of topological entropy for automorphisms will be studied. Automorphisms are the most basic objects associated to operator algebras, and they can reveal different facets of the same underlying object. The entropy is a numerical constant that distinguishes different automorphisms.Previous joint work of the proposer showed that the current theory, based on completely positive maps, can be better reformulated in terms of complete contractions. This puts the theory into a much more flexible situation where more general and powerful tools can be brought to bear on the problems of the field, notably relating to crossed products by automorphism groups. The modern study of operator algebras has evolved from two main sources. Matrices, which are generalizations of numbers, were introduced to solve equations and now find applications from computer graphics to search engines for the web. In formulating quantum mechanics mathematically, von Neumann found that he needed infinite dimensional versions of matrices called linear operators which were best studied in operator algebras. Moreover the time evolution of quantum mechanical systems came to be expressed in terms of the crossed product by groups of automorphisms, and here topological entropy plays an important role. The project is mainly concerned with the theoretical underpinnings of operator algebras, but the proposed work in these areas could impact some of these more concrete areas, since the finite factors are those operator algebras which most closely model matrices.
提出者将继续他的研究长期的Kadison-Ringrosecection上同调的冯诺依曼代数。他将使用和完善一些最近开发的技术需要显示某些多线性算子的完整有界性。调查的cohomologygroups自然导致最近推出的概念,赋范子代数,这一主题将继续,因为它直接适用于上同调和有界投影问题。在一个不同的,但相关的方向,极大交换子代数(masas)和一般的子代数冯诺依曼代数将研究。在联合工作中,提议者引入了强奇异masas的概念,并证明了许多由双曲群(包括自由群的一类)产生的有限因子具有这样的masas。到目前为止得到的结果表明,该理论现在可以扩展到研究一般的子代数。这直接关系到因子的结构(算子代数的构建块),这些研究领域的总体目标是增加我们在这一领域的理解。在以前完成的工作的基础上,将研究自同构的拓扑熵理论中的问题。自同构是与算子代数相关的最基本的对象,它们可以揭示同一底层对象的不同方面。熵是区分不同自同构的一个数值常数。提出者之前的联合工作表明,目前的理论,基于完全正映射,可以更好地重新表述为完全压缩。这使理论进入一个更加灵活的情况下,更普遍和强大的工具,可以承担的问题领域,特别是有关交叉产品的自同构群。 算子代数的现代研究有两个主要来源。矩阵是数字的一般化,它被用来解方程,现在从计算机图形学到网络搜索引擎都有应用。在制定量子力学数学,冯诺依曼发现,他需要无限维版本的矩阵称为线性算子,最好的研究在算子代数。此外,量子力学系统的时间演化可以用自同构群的交叉积来表示,其中拓扑熵起着重要作用。该项目主要关注算子代数的理论基础,但这些领域的拟议工作可能会影响其中一些更具体的领域,因为有限因子是那些最接近模型矩阵的算子代数。

项目成果

期刊论文数量(0)
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Roger Smith其他文献

Welfare versus Justice - Again!
福利与正义——再次!
  • DOI:
  • 发表时间:
    2005
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Roger Smith
  • 通讯作者:
    Roger Smith
HPA axis in the late-gestation ovine fetus? Urocortin: a mechanism for the sustained activation of the
妊娠晚期羊胎儿的 HPA 轴?
  • DOI:
  • 发表时间:
    2016
  • 期刊:
  • 影响因子:
    0
  • 作者:
    J. Challis;A. Holloway;D. Howe;G. Chan;V. Clifton;Roger Smith
  • 通讯作者:
    Roger Smith
Molecular Detection of Methicillin Resistant Staphylococcus Aureus Isolated From Hospital Patients and Food Handlers in FCT , North Central , Nigeria
尼日利亚中北部 FCT 医院患者和食品处理人员分离出的耐甲氧西林金黄色葡萄球菌的分子检测
  • DOI:
  • 发表时间:
    2018
  • 期刊:
  • 影响因子:
    0
  • 作者:
    M. M. Phillips;K. Krisciunas;N. Suntzeff;R. G. Abraham;M. G. Beckett;M. Bonati;P. Candia;T. Michael Corwin;D. Depoy;J. Espinoza;A. Firth;W. Freedman;G. Galaz;L. Germany;D. González;M. Hamuy;N. C. Hastings;Aimee L. Hungerford;Valentin D. Ivanov;Erika Labbé;R. Marzke;Patrick J. McCarthy;R. McMahon;R. Mcmillan;C. Muena;S. E. Persson;M. Roth;M. T. Ruiz;R. C. Smith;Roger Smith;L. Strolger;Christopher Stubbs
  • 通讯作者:
    Christopher Stubbs
Density functional study of Aun (n = 3–5) clusters on relaxed graphite surfaces
松弛石墨表面上 Aun (n = 3–5) 团簇的密度泛函研究
  • DOI:
    10.1016/j.susc.2004.11.044
  • 发表时间:
    2005
  • 期刊:
  • 影响因子:
    1.9
  • 作者:
    G. Wang;J. BelBruno;S. Kenny;Roger Smith
  • 通讯作者:
    Roger Smith
Atrial Natriuretic Peptide, Cyclic GMP Analogues and Modulation of Guanylyl Cyclase do not Alter Stimulated POMC Peptide Release From Perifused Rat or Sheep Corticotrophs
心房钠尿肽、环 GMP 类似物和鸟苷酸环化酶的调节不会改变灌注的大鼠或绵羊促肾上腺皮质激素刺激的 POMC 肽释放
  • DOI:
    10.1046/j.1365-2826.1997.00665.x
  • 发表时间:
    1997
  • 期刊:
  • 影响因子:
    3.2
  • 作者:
    M. Bowman;P. Robinson;Roger Smith
  • 通讯作者:
    Roger Smith

Roger Smith的其他文献

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{{ truncateString('Roger Smith', 18)}}的其他基金

Charge Quantizing CCDs Optimized for Astronomy
针对天文学优化的电荷量化 CCD
  • 批准号:
    2308380
  • 财政年份:
    2023
  • 资助金额:
    $ 15万
  • 项目类别:
    Standard Grant
Prototyping a New Telescope Design for Unprecedented Survey Speed in the Infrared
原型设计新型望远镜,实现前所未有的红外观测速度
  • 批准号:
    2010041
  • 财政年份:
    2020
  • 资助金额:
    $ 15万
  • 项目类别:
    Standard Grant
Modelling radiation resistant low activation High Entropy Alloys
抗辐射低活化高熵合金建模
  • 批准号:
    EP/S032819/1
  • 财政年份:
    2019
  • 资助金额:
    $ 15万
  • 项目类别:
    Research Grant
India - UK Civil Nuclear Collaboration: Development of Radiation Damage Resistant High Entropy Alloys for Advanced Nuclear Systems
印度-英国民用核合作:开发用于先进核系统的抗辐射损伤高熵合金
  • 批准号:
    EP/R021724/1
  • 财政年份:
    2018
  • 资助金额:
    $ 15万
  • 项目类别:
    Research Grant
Atomistic modelling and experimental verification of vitrified matrices for waste encapsulation
废物封装用玻璃化基质的原子建模和实验验证
  • 批准号:
    EP/K007882/1
  • 财政年份:
    2013
  • 资助金额:
    $ 15万
  • 项目类别:
    Research Grant
Intrasynovial soft tissue healing - a novel translational goal for mesenchymal stem cell therapy
滑膜内软组织愈合——间充质干细胞治疗的新转化目标
  • 批准号:
    MR/J006815/1
  • 财政年份:
    2012
  • 资助金额:
    $ 15万
  • 项目类别:
    Research Grant
Perturbations of Operator Algebras and Related Topics
算子代数的扰动及相关主题
  • 批准号:
    1101403
  • 财政年份:
    2011
  • 资助金额:
    $ 15万
  • 项目类别:
    Continuing Grant
Performance and Reliability of Metallic Materials for Nuclear Fission Power Generation
核裂变发电用金属材料的性能和可靠性
  • 批准号:
    EP/I003150/1
  • 财政年份:
    2010
  • 资助金额:
    $ 15万
  • 项目类别:
    Research Grant
Modelling absorption of electromagnetic radiation by carbon-based constituents of the interstellar medium
模拟星际介质碳基成分对电磁辐射的吸收
  • 批准号:
    EP/F016603/1
  • 财政年份:
    2008
  • 资助金额:
    $ 15万
  • 项目类别:
    Research Grant
Multiscale modelling and experimental investigation of radiation effects in oxides and heavy metals
氧化物和重金属辐射效应的多尺度建模和实验研究
  • 批准号:
    EP/F012047/1
  • 财政年份:
    2007
  • 资助金额:
    $ 15万
  • 项目类别:
    Research Grant

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Operator algebras and index theory in quantum walks and quantum information theory
量子行走和量子信息论中的算子代数和索引论
  • 批准号:
    24K06756
  • 财政年份:
    2024
  • 资助金额:
    $ 15万
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    Grant-in-Aid for Scientific Research (C)
Quantum singularity and non-linear positive maps on operator algebras
算子代数上的量子奇点和非线性正映射
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    23K03151
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    2023
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Categorical Symmetries of Operator Algebras
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  • 批准号:
    2247202
  • 财政年份:
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    Standard Grant
Conference: Groundwork for Operator Algebras Lecture Series 2023
会议:2023 年算子代数系列讲座的基础
  • 批准号:
    2247796
  • 财政年份:
    2023
  • 资助金额:
    $ 15万
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Conference: East Coast Operator Algebras Symposium 2023
会议:2023 年东海岸算子代数研讨会
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K-theory of Operator Algebras and Index Theory on Spaces of Singularities
算子代数的K理论与奇点空间索引论
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算子代数的新视野:有限维近似和量化函数理论
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    RGPIN-2022-03600
  • 财政年份:
    2022
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Conference: Groundwork for Operator Algebras Lecture Series (GOALS) 2022
会议:算子代数基础讲座系列 (GOALS) 2022
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Identities from Vertex Operator Algebras on the Moduli of Curves
曲线模上顶点算子代数的恒等式
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  • 财政年份:
    2022
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    $ 15万
  • 项目类别:
    Discovery Grants Program - Individual
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