Research of quantum group actions on operator algebras

2022 Fiscal Year Final Research Report

• Project/Area Number: 18K03317
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12010:Basic analysis-related
• Research Institution: Waseda University (2020-2022); Hokkaido University (2018-2019)
• Principal Investigator: Tomatsu Reiji 早稲田大学, 教育・総合科学学術院, 教授 (70447366)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Keywords: von Neumann環 / C*環 / 作用素環 / テンソル圏

Outline of Final Research Achievements

My research is to classify actions of C*-tensor categories on von Neumann algebras. The action here means a *-preserving tensor functor from the given category into the C*-tensor category consisting of endomorphisms on a von Neumann algebras. My main result is that we can classify centrally free cocycle actions on any von Neumann algebras up to approximately inner automorphisms. This result contains classification results for amenable discrete quantum groups of Kac type
which was proved before. Moreover, the main result also gives us another proof of classification of subfactors due to Popa.

Free Research Field

作用素環論

Academic Significance and Societal Importance of the Research Achievements

本研究で得られた結果は作用素環論やそれに関連する分野の発展に寄与するものである．現代社会の根底の部分を支えている数学のさらなる進展が見られたことに社会的意義がある．