A csomprehensive study of symmetries of operator algebras

• 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
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥17,290,000 (Direct Cost: ¥13,300,000、Indirect Cost: ¥3,990,000); Fiscal Year 2014: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2013: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2012: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2011: ¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000); Fiscal Year 2010: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
• Keywords: 函数解析 / 作用素環 / 群作用 / 国際研究者交流 / K理論 / 作用素環論 / 郡作用 / 部分因子環 / C*-環 / K-理論 / テンソル圏

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.

Research Products

• [Journal Article] Indecomposable characters of infinite dimensional groups associated with operator algebras (2016)
  • Author(s): Takumi Enomoto and Masaki Izumi
  • Journal Title: Journal of Mathematical Society of Japan Volume: 未定
  • NAID: 130005166146
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Subfactors of index exactly 5 (2015)
  • Author(s): Masaki Izumi, Scott Morrison, David Penneys, Emily Peters, and Noah Snyder
  • Journal Title: Bulletin of London Mathematical Society Volume: 未定
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Remarks on free mutual information and orbital free entropy (2015)
  • Author(s): Masaki Izumi and Yoshimichi Ueda
  • Journal Title: Nagoya Mathematical Journal Volume: 未定
  • NAID: 120006716057
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] ON EXTENDABILITY OF ENDOMORPHISMS AND OF <i>E</i>₀-SEMIGROUPS ON FACTORS (2014)
  • Author(s): P. Bikram, M. Izumi, R. Srinivasan, and V. S. Sunder
  • Journal Title: Kyushu Journal of Mathematics Volume: 68 Issue: 1 Pages: 165-179
  • DOI: 10.2206/kyushujm.68.165
  • NAID: 130004941523
  • ISSN: 1340-6116, 1883-2032
  • Peer Reviewed
• [Journal Article] Subfactors of index less than 5, Part 3: Quadruple points (2012)
  • Author(s): Izumi, Masaki
  • Journal Title: Communications in Mathematical Physics Volume: 316 Issue: 2 Pages: 531-554
  • DOI: 10.1007/s00220-012-1472-5
  • Peer Reviewed
• [Journal Article] E0-semigroups: around and beyond Arveson's work (2012)
  • Author(s): Izumi, Masaki
  • Journal Title: Journal of Operator theory Volume: 68 Pages: 335-363
• [Journal Article] Quasi-free actions of finite groups on the Cuntz algebra O_∞ (2011)
  • Author(s): P.Goldstein, M.Izumi
  • Journal Title: Tohoku Mathematical Journal Volume: 63 Pages: 729-749
  • Peer Reviewed
• [Journal Article] Z^<2->actions on Kirchberg algebras (2010)
  • Author(s): Masaki Izumi, Horoki Matui
  • Journal Title: Advances in Mathematics Volume: 224 Pages: 355-400
  • Peer Reviewed
• [Presentation] 3^n11 subfactors (2014)
  • Author(s): Maaki Izumi
  • Organizer: Subfactor Theory in Mathematics and Physics
  • Place of Presentation: University of Hawai'i Maui College
  • Year and Date: 2014-07-14 – 2014-07-18
  • Invited
• [Presentation] Classification of subfactors and fusion categories (2014)
  • Author(s): Masaki Izumi
  • Organizer: The international conference on operator algebras and mathematical physics
  • Place of Presentation: 大連工科大学
  • Year and Date: 2014-06-14 – 2014-06-17
  • Invited
• [Presentation] Near group categories and their relatives: Cuntz algebra approach (2014)
  • Author(s): Masaki Izumi
  • Organizer: Subfactors, CFT, and VOA
  • Place of Presentation: Vandelbilt University
  • Year and Date: 2014-05-02 – 2014-05-08
  • Invited
• [Presentation] The classification of 3^n subfactors with odd n (2014)
  • Author(s): Masaki Izumi
  • Organizer: Subfactors and Fusion Categories
  • Place of Presentation: Banff International Research Station
  • Year and Date: 2014-04-14 – 2014-04-18
  • Invited
• [Presentation] Indecomposable characters of infinite dimensional groups associated with operator algebras (2013)
  • Author(s): Masaki Izumi
  • Organizer: Workshop on Operator Algebras
  • Place of Presentation: 東京大学
  • Invited
• [Presentation] Group actions on operator algebras (2013)
  • Author(s): Masaki Izumi
  • Organizer: The Asian Mathematical Conference
  • Place of Presentation: Busan, Korea
  • Invited
• [Presentation] Group actions on Kirchberg algebras (2013)
  • Author(s): Masaki Izumi
  • Organizer: Mathematics and Quantum Physics
  • Place of Presentation: Rome, Italy
  • Invited
• [Presentation] Sunfactors of index 5 and beyond 5 (2012)
  • Author(s): M.Izumi
  • Organizer: Conference on von Neumann algebras and related topics
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2012-01-10
• [Presentation] Group-subgroup subfactors revisited (2012)
  • Author(s): Izumi, Masaki
  • Organizer: SunderFest
  • Place of Presentation: The Institute of Mathematical Sciences, Chennai, India
  • Invited
• [Presentation] Group actions on operator algebras (2012)
  • Author(s): Izumi, Masaki
  • Organizer: London Mathematical Society Midlands Regional Meeting
  • Place of Presentation: Aberystwyth University, UK
  • Invited
• [Presentation] The classification of certain fusion categories and subfactors, I, II (2012)
  • Author(s): Izumi, Masaki
  • Organizer: Quantum Probabilistic Symmetries
  • Place of Presentation: Aberystwyth University, UK
  • Invited
• [Presentation] Noncommutative Poisson boundary (2012)
  • Author(s): Izumi, Masaki
  • Organizer: Levi-Civita Colloquia
  • Place of Presentation: Center for Mathematics and Theoretical Physics, Rome, Italy
  • Invited
• [Presentation] Poly-Z group actions on Kirchberg algebras (2012)
  • Author(s): Izumi, Masaki
  • Organizer: C*-algebras, Dynamics, and Classification
  • Place of Presentation: The Mathematisches Forschungsinstitut Oberwolfach. Germany
  • Invited
• [Presentation] Type III E_0-semigroups (2011)
  • Author(s): M.Izumi
  • Organizer: Winter school of operator algebras
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2011-12-07
• [Presentation] Discrete group actions on Kirchberg algebras (2011)
  • Author(s): M.Izumi
  • Organizer: Conference on C^*-algebras and related topics
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2011-09-05
• [Presentation] Goldman's type results for subfactors revisited (2011)
  • Author(s): M.Izumi
  • Organizer: II_1 factors : rigidity, symmetries and classification
  • Place of Presentation: アンリポワンカレ研究所、パリ、フランス(招待講演)
  • Year and Date: 2011-05-26
• [Presentation] Toeplitz CAR flows (2010)
  • Author(s): Masaki Izumi
  • Organizer: 作用素論・作用素環論研究集会
  • Place of Presentation: 東京理科大森戸記念会館、東京都(招待講演)
  • Year and Date: 2010-11-14
• [Presentation] Group actions on operator algebras (2010)
  • Author(s): Masaki Izumi
  • Organizer: International Congress of Mathematicians
  • Place of Presentation: The Hyderabad International Convention Centre, Hyderabad, India(招待講演)
  • Year and Date: 2010-08-20
• [Presentation] Noncommutative Poisson boundaries (2010)
  • Author(s): Masaki Izumi
  • Organizer: International Conference of Quantum Probability and Related Topics
  • Place of Presentation: Jawaharal Nehru Centre for Advanced Scientific Research, Bangalore, India(招待講演)
  • Year and Date: 2010-08-15
• [Presentation] The Toeplitz CAR flows (2010)
  • Author(s): Masaki Izumi
  • Organizer: Satellite Conference on Operator Algebras
  • Place of Presentation: The institute of Mathematical Sciences, Chennai, India(招待講演)
  • Year and Date: 2010-08-13
• [Presentation] Classification of group actions on Kirchberg algebras (2010)
  • Author(s): Masaki Izumi
  • Organizer: The Special Week on Operator Algebras
  • Place of Presentation: 華東師範大学、上海、中華人民共和国(招待講演)