"Measure-theoretic dimension groups, classification of ergodic transformation, and topics in positivity"

“测度论维度组、遍历变换的分类以及积极性主题”

• 批准号: 3130-2012
• 负责人: Handelman, David
• 金额: $ 0.87万
• 依托单位: University of Ottawa
• 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: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=568276
• 关键词: Measure; theoretic; dimension; groups; classification

A new invariant, a "dimension space", developed (2009) by Giordano and me for classifying (measure-theoretically) dynamical systems leads to new results, questions, novel directions of research, and to other areas of mathematics. The project is mostly concerned with developing a lexicon between properties of ergodic transformations and (more algebraic/functional analytic) properties of dimension spaces, so that properties that are more easily seen in one context can be be translated to the other.

一个新的不变量，一个“维空间”，由佐丹奴和我开发（2009年）分类（测量理论）动力系统导致新的结果，问题，新的研究方向，以及其他数学领域。该项目主要关注遍历变换的性质和维度空间的（更多代数/函数分析）性质之间的词典，以便在一个上下文中更容易看到的性质可以被翻译到另一个。