A csomprehensive study of symmetries of operator algebras

2014 Fiscal Year Final Research Report

• Project/Area Number: 22340032
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Kyoto University
• Principal Investigator: IZUMI Masaki 京都大学, 理学(系)研究科(研究院), 教授 (80232362)
• Co-Investigator(Renkei-kenkyūsha): KAWAHIGASHI Yasuyuki 東京大学, 数理科学研究科, 教授 (90214684) ; UEDA Yoshimichi 九州大学, 数理学研究院, 准教授 (00314724) ; MATUI Hiroki 千葉大学, 理学研究科, 教授 (40345012) ; OZAWA Narutaka 京都大学, 数理解析研究所, 教授 (60323466) ; OKAYASU Rui 大阪教育大学, 教育学部, 准教授 (70362746) ; TOMATSU Reiji 北海道大学, 理学研究科, 准教授 (70447366) ; KIDA Yoshikata 京都大学, 理学研究科, 准教授 (90451517) ; YAMAGAMI Shigeru 名古屋大学, 多元数理科学研究科, 教授 (90175654)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 函数解析 / 作用素環 / 群作用

Outline of Final Research Achievements

I studied the structure of symmetries of operator algebras. With Hiroki Matui, we studied discrete group actions on C*-algebras, and partially obtained a classification invariant by using topological properties of discrete groups and the automorphism groups of C*-algebras.
With Vaughan Jones, Scott Morrison, David Penneys, Emily Peters, Noah Snyder, we completely classified subfactors of index less than or equal to 5. With Pinhas Grossman and Noah Snyder, we gave detailed description of the structure of the Morita equivalence class of the fusion categories arising from the Asaeda-Haagerup subfactors.

Free Research Field

作用素環論