Study of operator algebras and dynamical systems from various perspectives

• Project/Area Number: 26400108
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Chiba University
• Principal Investigator: Matui Hiroki 千葉大学, 大学院理学研究院, 教授 (40345012)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 作用素環 / 極小力学系 / 群作用

Outline of Final Research Achievements

I studied operator algebras and dynamical systems from various perspectives. In particular, I focused on classification of group actions on simple nuclear C*-algebras and analysis of minimal dynamical systems on Cantor sets. For instance, I obtained a complete classification of outer actions of poly-Z-groups on Kirchberg algebras up to cocycle conjugacy. Secondly, I classified etale groupoids arising from finite products of shifts of finite type, and computed the homology groups of the etale groupoids and the abelianizations of the associated topological full groups.

Research Products

• [Journal Article] Full groups of Cuntz-Krieger algebras and Higman-Thompson groups (2017)
  • Author(s): Kengo Matsumoto and Hiroki Matui
  • Journal Title: Groups, Geometry, and Dynamics Volume: 11 Issue: 2 Pages: 499-531
  • DOI: 10.4171/ggd/405
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Continuous orbit equivalence of topological Markov shifts and dynamical zeta functions (2016)
  • Author(s): Kengo Matsumoto and Hiroki Matui
  • Journal Title: Ergodic Theory and Dynamical Systems Volume: 36 Issue: 5 Pages: 1557-1581
  • DOI: 10.1017/etds.2014.128
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Etale groupoids arising from products of shifts of finite type (2016)
  • Author(s): H. Matui
  • Journal Title: Adv. Math. Volume: 303 Pages: 502-548
  • DOI: 10.1016/j.aim.2016.08.023
  • Peer Reviewed
• [Journal Article] The Rokhlin property vs. Rokhlin dimension 1 on unital Kirchberg algebras (2015)
  • Author(s): S. Barlak, D. Enders, H. Matui, G. Szabo, W. Winter
  • Journal Title: J. Noncommut. Geom. Volume: 9
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Universal properties of group actions on locally compact spaces (2015)
  • Author(s): H. Matui, M. Rordam
  • Journal Title: J. Funct. Anal. Volume: 268 Issue: 12 Pages: 3601-3648
  • DOI: 10.1016/j.jfa.2015.01.022
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Topological full groups of one-sided shifts of finite type (2015)
  • Author(s): H. Matui
  • Journal Title: J. Reine Angew. Math. Volume: 705 Issue: 705 Pages: 35-84
  • DOI: 10.1515/crelle-2013-0041
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Z-stability of crossed products by strongly outer actions II (2014)
  • Author(s): H. Matui, Y. Sato
  • Journal Title: Amer. J. Math. Volume: 136
  • Peer Reviewed
• [Journal Article] Decomposition rank of UHF-absorbing C*-algebras (2014)
  • Author(s): H. Matui, Y. Sato
  • Journal Title: Duke Math. J. Volume: 163
  • Peer Reviewed
• [Journal Article] Topological full groups of C*-algebras arising from beta-expansions (2014)
  • Author(s): K. Matsumoto, H. Matui
  • Journal Title: J. Aust. Math. Soc. Volume: 97
  • Peer Reviewed
• [Journal Article] Continuous orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras (2014)
  • Author(s): K. Matsumoto, H. Matui
  • Journal Title: Kyoto J. Math. Volume: 54
  • Peer Reviewed
• [Presentation] Topological full groups and C*-algebras (2016)
  • Author(s): H. Matui
  • Organizer: International Conference for the 70th Anniversary of Korean Mathematical Society
  • Place of Presentation: ソウル（韓国）
  • Year and Date: 2016-10-22
  • Int'l Joint Research / Invited
• [Presentation] Poly-Z group actions on Kirchberg algebras (2016)
  • Author(s): H. Matui
  • Organizer: MSJ-SI "Operator Algebras and Mathematical Physics"
  • Place of Presentation: 東北大学（宮城県仙台市）
  • Year and Date: 2016-08-01
  • Int'l Joint Research / Invited
• [Presentation] Topological full groups of etale groupoids (2016)
  • Author(s): 松井宏樹
  • Organizer: エルゴード理論と群論に関連した作用素環論における諸問題の研究
  • Place of Presentation: 京都大学数理解析研究所（京都府、京都市）
  • Year and Date: 2016-01-25
  • Invited
• [Presentation] Various examples of topological full groups (2015)
  • Author(s): H. Matui
  • Organizer: Growth, Symbolic Dynamics and Combinatorics of Words in Groups
  • Place of Presentation: Ecole Normale Superieure（フランス、パリ）
  • Year and Date: 2015-06-01
  • Int'l Joint Research / Invited