Mathematics

数学

• 批准号: CRC-2014-00029
• 负责人: Elliott, George
• 金额: $ 14.57万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Canada Research Chairs
• 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: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=695428
• 关键词: Mathematics

The objective of the proposed research is to verify a rather striking phenomenon that I have recently observed. Considerable evidence has now been assembled that a large class of quite complicated mathematical objects---virtually all naturally arising norm-closed algebras in Hilbert space (including those of interest in mathematical physics, and in other branches of mathematics in which complex systems are considered, such as the theory of dynamical systems and the theory of foliations)---can be completely described in terms of simple data---the so-called K-theory invariant, sometimes now referred to as the Elliott invariant. On the one hand, this is most unexpected. (But the evidence is overwhelming.) On the other hand, this discovery has far-reaching implications, both for the class of objects involved (in technical terms, the class of amenable C*-algebras), and, it appears likely, for the related areas of mathematics and physics in which these objects appear. (For instance, this simple behaviour can be detected in the orbit structure of dynamical systems.)

拟议研究的目的是验证我最近观察到的一个相当惊人的现象。现在有相当多的证据表明，一大批相当复杂的数学对象——几乎所有在希尔伯特空间中自然产生的模闭代数（包括那些对数学物理感兴趣的代数，以及那些考虑复杂系统的数学分支，如动力系统理论和叶理理论）——都可以用简单数据——即所谓的k理论不变量——来完全描述。有时也被称为艾略特不变量。一方面，这是最出乎意料的。（但证据确凿。）另一方面，这一发现具有深远的意义，无论是对所涉及的对象类别（用专业术语来说，是可调节的C*代数类别），还是对这些对象出现的相关数学和物理领域。（例如，这种简单的行为可以在动力系统的轨道结构中检测到。）