Operator Algebras and Dynamics
算子代数和动力学
基本信息
- 批准号:105463-2012
- 负责人:
- 金额:$ 2.19万
- 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:2015
- 资助国家:加拿大
- 起止时间:2015-01-01 至 2016-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
In the 1980's, A. Connes introduced noncommutative spaces, and began to develop noncommutative geometry, a rapidly growing new area of mathematics which contributes to many disciplines in mathematics and physics. A large source of examples of noncommutative spaces is given by the quotient of equivalence relations. With I.F. Putnam, C.F. Skau and more recently H. Matui, I have extensively studied the noncommutative spaces associated to minimal homeomorphisms on a Cantor set. We plan to pursue the study of orbit equivalence for larger class of minimal actions.
Connes and Woods introduced a new property of ergodic theory called approximate transitivity (AT) to
characterize a class of von Neumann algebras. They noted also that the Poisson boundary of some random walks is AT. Recently D.E. Handelman and I defined dimension spaces, a measure theoretic version of dimension groups. Using this new notion, we will continue the study of AT(k)_actions, a generalized verson of approximate transitivity and of the Poisson boundary of matrix-valued random walks.
One of most important recent development in the theory of C*-algebras is Elliott's classification scheme of amenable C*-algebras. His starting point was an example by Blackadar of a non approximately finite (AF) sub C*-algebra of an AF algebra. I want to study the real C*-algebra equivalent to both Blackadar's example and Elliott's program.
Several properties of von Neumann algebras and C*-algebras translate in properties of their unitary groups. I plan to continue to study and extend this correspondence for both C*-algebras and von Neumann algebras.
The notion of sofic groups, introduced by Gromov and Weiss, was extended to measurable actions of groups and to measurable equivalence relations. In this research I will study properties of the full group asociated to sofic equivalence relations
20世纪80年代,A. Connes引入了非交换空间,并开始发展非交换几何,这是一个快速发展的数学新领域,对数学和物理的许多学科做出了贡献。非交换空间的例子的大量来源是由等价关系的商给出的。与 I.F.普特南,C.F. Skau 和最近的 H. Matui,我广泛研究了与康托集上的最小同胚相关的非交换空间。我们计划继续研究更大类别的最小作用的轨道等效性。
Connes 和 Woods 引入了遍历理论的一个新属性,称为近似传递性 (AT)
描述一类冯诺依曼代数的特征。他们还指出,一些随机游走的泊松边界是 AT。最近D.E.汉德曼和我定义了维度空间,即维度组的测度理论版本。使用这个新概念,我们将继续研究 AT(k)_actions,这是近似传递性和矩阵值随机游走的泊松边界的广义版本。
C* 代数理论最近最重要的发展之一是 Elliott 的 C* 代数分类方案。他的出发点是 Blackadar 的一个 AF 代数的非近似有限 (AF) 子 C* 代数的例子。我想研究真正的 C* 代数,相当于 Blackadar 的例子和 Elliott 的程序。
冯·诺依曼代数和 C* 代数的几个性质转化为其酉群的性质。我计划继续研究并扩展 C* 代数和冯诺依曼代数的对应关系。
格罗莫夫和韦斯提出的 sofic 群的概念被扩展到群的可测量的行为和可测量的等价关系。在这项研究中,我将研究与 sofic 等价关系相关的整个群的属性
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:
$ 2.19万 - 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:
$ 2.19万 - 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:2020
- 资助金额:
$ 2.19万 - 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:
$ 2.19万 - 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:
$ 2.19万 - 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:
$ 2.19万 - 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:
$ 2.19万 - 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:
$ 2.19万 - 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:
$ 2.19万 - 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:
$ 2.19万 - 项目类别:
Discovery Grants Program - Individual
相似海外基金
Interactions between operator algebras and topological dynamics
算子代数与拓扑动力学之间的相互作用
- 批准号:
2750740 - 财政年份:2022
- 资助金额:
$ 2.19万 - 项目类别:
Studentship
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:
$ 2.19万 - 项目类别:
Standard Grant
Topology and Measure in Dynamics and Operator Algebras
动力学和算子代数中的拓扑和测度
- 批准号:
1800633 - 财政年份:2018
- 资助金额:
$ 2.19万 - 项目类别:
Continuing Grant
U.S. Participation in the Centre de Recerca Matematica Research Program Operator Algebras: Dynamics and Interactions
美国参与 Center de Recerca Matematica 研究计划算子代数:动力学与相互作用
- 批准号:
1665118 - 财政年份:2017
- 资助金额:
$ 2.19万 - 项目类别:
Standard Grant
Soficity, Dynamics, and Operator Algebras
Soficity、动力学和算子代数
- 批准号:
1600717 - 财政年份:2016
- 资助金额:
$ 2.19万 - 项目类别:
Standard Grant
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:
$ 2.19万 - 项目类别:
Discovery Grants Program - Individual
Amenabilty, soficity, dynamics, and operator algebras
适应性、社交性、动力学和算子代数
- 批准号:
1500593 - 财政年份:2015
- 资助金额:
$ 2.19万 - 项目类别:
Continuing Grant
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:
$ 2.19万 - 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:
$ 2.19万 - 项目类别:
Discovery Grants Program - Individual














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