Structures of crossed products of minimal dynamical systems based on subalgebra families

2018 Fiscal Year Final Research Report

• Project/Area Number: 17H06737
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Nagoya University
• Principal Investigator: Suzuki Yuhei 名古屋大学, 多元数理科学研究科, 助教 (20804511)
• Project Period (FY): 2017-08-25 – 2019-03-31
• Keywords: 接合積C*環 / 非可分作用素環 / 中間因子 / 中間作用素環 / 位相力学系 / 完全性

Outline of Final Research Achievements

I have solved a few famous problems by Delaroche, Farah--Katsura et al. I also solved a well-known question either the AP implies exactness for general locally compact groups (the answer is yes). Furthermore I was able to find a new phenomena about the complete correspoindence between intermediate extensions of dynamical systems and intermediate operator algebras of the associated crossed product inclusions. All these problems and phenomena are left open/unknown for more than 10 years.

Free Research Field

作用素環

Academic Significance and Societal Importance of the Research Achievements

今回の採択課題の研究で得られた成果は，いずれもこれまでには専門家にとっても想像することすら難しかった興味深い例の構成や，新しい現象の発見，確立，既存の有用な概念同士の関係の確立である．これらの成果はすでにいくつかの有力な研究者により活用され，さらなる発展が研究対象とされており，学術的な意義・インパクトの大きさを早くも実感することができている．