Research of automorphism groups and group action classification of operator algebras

2015 Fiscal Year Final Research Report

• Project/Area Number: 23540246
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: Kyushu University
• Principal Investigator: Masuda Toshihiko 九州大学, 数理(科)学研究科(研究院), 准教授 (60314978)
• Co-Investigator(Renkei-kenkyūsha): Tomatsu Reiji 北海道大学, 理学研究科, 准教授 (70447366)
• Project Period (FY): 2011-04-28 – 2016-03-31
• Keywords: 作用素環 / 群作用 / 一径数自己同型群 / 離散従順群 / コンパクト群

Outline of Final Research Achievements

| mainly study group actions on operator algebras. As a results, I first obtained a unified proof of classification theorem of discrete amenable group actions on injective factors. Next, I classified one-parameter automorphism groups with Rohlin property with Reiji Tomatsu. As one application, we present a proof of uniqueness of the injective factor of type III_1 from point of view of structure theorem of factors. I also study classification of compact group actions on injective factors with Reiji Tomatsu. In particular, we obtained classification theorem of actions of groups with nice topological property, e.g., compact Lie groups.

Free Research Field

作用素環