Research of symmetries arising from automorphisms of operator algebras

2022 Fiscal Year Final Research Report

• Project/Area Number: 16K05180
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyushu University
• Principal Investigator: Masuda Toshihiko 九州大学, 数理学研究院, 教授 (60314978)
• Project Period (FY): 2016-04-01 – 2023-03-31
• Keywords: 因子環 / 自己同型群 / 対称性 / 群作用

Outline of Final Research Achievements

I studied the symmetries of operator algebras by focusing on automorphism groups of operator algebras. I obtained the following results mainly. 1. Classification of Roberts actions of tensor categories on the injective type III_1 factor. 2. I solved the conjecture of Ando-Haagerup-Houdayer-Marakech about the flows of relative bicentralizer associated with inclusion of type III_1 factors when small algebra is injective. 3. I classified outer actions (G-kernels) of discrete amenable groupoids on injective factors. My proof does not require the method of model actions to get rid of obstraction, and it is more natural. 4. I classified actions of discrete amenable groups on orbit equivalence of ergodic theory.

Free Research Field

作用素環論

Academic Significance and Societal Importance of the Research Achievements

私の研究によって、作用素環の群作用や自己同型群の対称性の理解がより深まった。特にテンソル圏との関連において深い理解が得られたと考える。またエルゴード理論のように作用素環と関連する分野においても、作用素環論に由来するアイディアが有効に使えることも明確となり、理論の発展に大きく寄与した。