Operator algebras and dynamical systems
算子代数和动力系统
基本信息
- 批准号:RGPIN-2018-06855
- 负责人:
- 金额:$ 1.68万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2020
- 资助国家:加拿大
- 起止时间:2020-01-01 至 2021-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
In the 1980's, A. Connes introduced non-commutative spaces, and began to develop non-commutative geometry. Today non-commutative geometry a rapidly growing new area of mathematics that contributes to many fields in mathematics and physics. A large source of examples of non-commutative spaces is associated to free minimal actions, up to orbit equivalence, of group of transformations of a topological space. The Bratteli-Vershik model has been a key tool in our study (with I.F. Putnam and C.F. Skau) of topological orbit equivalence of Cantor minimal systems. We plan to extend the Bratteli-Vershik construction to free minimal actions of other groups of homeomorphisms.
Several properties of von Neumann and C*-algebras translate in properties of their unitary groups. I plan to continue to study and extend such correspondences for both C*-algebras and von Neumann algebras in collaboration with P. W. Ng and with A. Sierakowski.
One of most important recent development in the theory of C*-algebras is Elliott's classification scheme of amenable C*-algebras. As real C*-algebras and their K-theoretical invariants play an increasingly important role in physics, I plan to enlarge the class of amenable real C*-algebras already classified by their corresponding Elliott's invariant.
Connes and Woods introduced a new property in ergodic theory called approximate transitivity (AT) to characterize a class of von Neumann algebras. They also noted that the asymptotic boundary of a random walk is AT. I will continue the study of AT and also of the asymptotic boundary of random walks on groups. Then with J. Renault I will analyse the asymptotic boundary of a random walk on a groupoid. Using the notion of dimension spaces, a measure theoretic version of dimension groups, I introduced with D.E. Handelman, we will continue the study of AT(k)_actions, a generalized version of approximate transitivity and of the Poisson boundary of matrix-valued random walks.
20世纪80年代,A.康纳斯介绍了非交换空间,并开始发展非交换几何。今天,非对易几何是一个迅速发展的新的数学领域,对数学和物理学的许多领域都有贡献。非交换空间的大量例子与拓扑空间的变换群的自由极小作用(直到轨道等价)有关。Bratteli-Vershik模型一直是我们研究的关键工具(与I.F. Putnam和C.F. Skau)关于Cantor极小系统的拓扑轨道等价性。我们计划将Bratteli-Vershik构造扩展到其他同胚群的自由极小作用。
冯诺依曼和C*-代数的一些性质转化为它们的酉群的性质。我计划继续研究和推广这种对应的C*-代数和冯诺依曼代数在合作P。Ng和A.谢拉科夫斯基
C ~*-代数理论的一个重要发展是Elliott提出的顺从C ~*-代数的分类方案。由于真实的C*-代数和它们的K-理论不变量在物理学中起着越来越重要的作用,我计划扩大已经由它们相应的Elliott不变量分类的顺从的真实的C*-代数的类。
Connes和Woods在遍历理论中引入了一个新的性质,称为近似传递性(AT)来刻画一类von Neumann代数。他们还指出,随机游走的渐近边界是AT。我将继续研究的AT和渐近边界的随机游动的群体。然后与雷诺我将分析的渐近边界的随机游动的广群。使用维数空间的概念,维数群的测度论版本,我介绍了与D. E。Handelman,我们将继续研究AT(k)作用,近似传递性和矩阵值随机游动的Poisson边界的推广版本。
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)
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Giordano, Thierry其他文献
Validating the City Region Food System Approach: Enacting Inclusive, Transformational City Region Food Systems
- DOI:
10.3390/su10051680 - 发表时间:
2018-05-01 - 期刊:
- 影响因子:3.9
- 作者:
Blay-Palmer, Alison;Santini, Guido;Giordano, Thierry - 通讯作者:
Giordano, Thierry
Giordano, Thierry的其他文献
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{{ truncateString('Giordano, Thierry', 18)}}的其他基金
Operator algebras and dynamical systems
算子代数和动力系统
- 批准号:
RGPIN-2018-06855 - 财政年份:2022
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Operator algebras and dynamical systems
算子代数和动力系统
- 批准号:
RGPIN-2018-06855 - 财政年份:2021
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Operator algebras and dynamical systems
算子代数和动力系统
- 批准号:
RGPIN-2018-06855 - 财政年份:2019
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Operator algebras and dynamical systems
算子代数和动力系统
- 批准号:
RGPIN-2018-06855 - 财政年份:2018
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Operator Algebras and Dynamics
算子代数和动力学
- 批准号:
105463-2012 - 财政年份:2016
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Operator Algebras and Dynamics
算子代数和动力学
- 批准号:
105463-2012 - 财政年份:2015
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Operator Algebras and Dynamics
算子代数和动力学
- 批准号:
105463-2012 - 财政年份:2014
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Operator Algebras and Dynamics
算子代数和动力学
- 批准号:
105463-2012 - 财政年份:2013
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Operator Algebras and Dynamics
算子代数和动力学
- 批准号:
105463-2012 - 财政年份:2012
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Topological orbit equivalence, amenability, approximate transitivity, antiautomorphisms, unitary groups and operator algebras
拓扑轨道等价、顺应性、近似传递性、反自同构、酉群和算子代数
- 批准号:
105463-2007 - 财政年份:2011
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
相似国自然基金
数学物理中精确可解模型的代数方法
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- 批准年份:2017
- 资助金额:48.0 万元
- 项目类别:面上项目
相似海外基金
Operator algebras and dynamical systems
算子代数和动力系统
- 批准号:
RGPIN-2018-06855 - 财政年份:2022
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Operator algebras and dynamical systems
算子代数和动力系统
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CRC-2015-00121 - 财政年份:2022
- 资助金额:
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Canada Research Chairs
Dynamical systems with singularities and operator algebras
具有奇点和算子代数的动力系统
- 批准号:
22K03354 - 财政年份:2022
- 资助金额:
$ 1.68万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Operator algebras and dynamical systems
算子代数和动力系统
- 批准号:
RGPIN-2018-06855 - 财政年份:2021
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Operator Algebras And Dynamical Systems
算子代数和动力系统
- 批准号:
CRC-2015-00121 - 财政年份:2021
- 资助金额:
$ 1.68万 - 项目类别:
Canada Research Chairs
Operator algebras and dynamical systems
算子代数和动力系统
- 批准号:
CRC-2015-00121 - 财政年份:2020
- 资助金额:
$ 1.68万 - 项目类别:
Canada Research Chairs
There and back again: operator algebras, algebras and dynamical systems
来来回回:算子代数、代数和动力系统
- 批准号:
DP200100155 - 财政年份:2020
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Projects
Operator algebras and dynamical systems
算子代数和动力系统
- 批准号:
CRC-2015-00121 - 财政年份:2019
- 资助金额:
$ 1.68万 - 项目类别:
Canada Research Chairs
Operator algebras and dynamical systems
算子代数和动力系统
- 批准号:
RGPIN-2018-06855 - 财政年份:2019
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Operator algebras and dynamical systems
算子代数和动力系统
- 批准号:
RGPIN-2018-06855 - 财政年份:2018
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual