Classification of operator algebras arising from minimal dynamical systems and topological orbit equivalence of minimal dynamical systems

• Project/Area Number: 18740085
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Chiba University
• Principal Investigator: MATUI Hiroki Chiba University, 大学院・理学研究科, 准教授 (40345012)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥270,000); Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000); Fiscal Year 2006: ¥1,600,000 (Direct Cost: ¥1,600,000)
• Keywords: 作用素環 / 極小力学系 / 軌道同型 / 群作用

Research Abstract

0次元の空間と言うべきカントール集合上の、極小力学系について研究した。具体的には、有限生成アーベル群のカントール集合への極小作用を、軌道同型で分類することに成功した。また、自由アーベル群の作用素環への作用を研究し、ある種のクラスの作用を分類することにも成功した。

Research Products

• [Journal Article] An absorption theorem for minimal AF equivalence relations on Cantor sets (2008)
  • Author(s): H. Matui
  • Journal Title: J. Math. Soc. Japan 60 Pages: 1171-1185
  • NAID: 10024905383
  • Peer Reviewed
• [Journal Article] Classification of outer actions of Z N on 0_2 (2008)
  • Author(s): H. Matui
  • Journal Title: Adv. Math. 217 Pages: 2872-2896
  • Peer Reviewed
• [Journal Article] Classification of uniformly outer actions of Z^2 on UHF algebras (2008)
  • Author(s): T. Katsura and H. Matui
  • Journal Title: Adv. Math. 218 Pages: 940-968
  • Peer Reviewed
• [Journal Article] The absorption theorem for affable equivalence relations (2008)
  • Author(s): T. Giordano, H. Matui, I. F. Putnam and C. F. Skau
  • Journal Title: Ergodic Theory Dynam. Systems 28 Pages: 1509-1531
  • Peer Reviewed
• [Journal Article] Orbit equivalence for Cantor minimal Z^2-systems (2008)
  • Author(s): T. Giordano, H. Matui, I. F. Putnamand C. F. Skau
  • Journal Title: J. Amer. Math. Soc. 21 Pages: 863-892
  • Peer Reviewed
• [Journal Article] Torsion in coinvariants of certain Canto: minimal Z^2-systems (2008)
  • Author(s): H. Matui
  • Journal Title: Trans. Amer. Math. Soc. 360 Pages: 4913-4928
  • Peer Reviewed
• [Journal Article] Torsion in coinvariants of certain Cantor minimal Z^2-systems (2008)
  • Author(s): H. Matui
  • Journal Title: Trans. Amer. Math. Soc 360, No. 9 Pages: 4913-4928
  • Peer Reviewed
• [Journal Article] Orbit equivalence for Cantor minimal Z^2-systems (2008)
  • Author(s): T. Giordano, H. Matui, I. F. Putnam and C. F. Skau
  • Journal Title: J. Amer. Math. Soc 21, No. 3 Pages: 863-892
  • Peer Reviewed
• [Journal Article] The absorption theorem for affable equivalence relations (2008)
  • Author(s): T. Giordano, H. Matui, I. F. Putnam and C. F. Skau
  • Journal Title: Ergodic Theory Dynam. Systems 28, No. 5 Pages: 1509-1531
  • Peer Reviewed
• [Journal Article] Classification of uniformly outer actions of Z^2 on UHF algebras (2008)
  • Author(s): T. Katsura and H. Matui
  • Journal Title: Adv. Math 218, No. 3 Pages: 940-968
  • Peer Reviewed
• [Journal Article] An absorption theorem for minimal AF equivalence relations on Cantor sets (2008)
  • Author(s): H. Matui
  • Journal Title: J. Math. Soc. Japan 60, No. 4 Pages: 1171-1185
  • NAID: 10024905383
  • Peer Reviewed
• [Journal Article] Classification of outer actions of Z^N an O_2 (2008)
  • Author(s): H. Matui
  • Journal Title: Advances in Mathematics 217,No.6 Pages: 2872-2896
  • Peer Reviewed
• [Journal Article] A short proof of affability for certain Cantor minimal Z^2-systems (2007)
  • Author(s): H. Matui
  • Journal Title: Canad. Math. Bull. 50 Pages: 418-426
  • Peer Reviewed
• [Journal Article] A short proof of affability for certain Cantor minimal Z^2-systems (2007)
  • Author(s): H. Matui
  • Journal Title: Canadian Mathematical Bulletin 50,No.3 Pages: 418-426
  • Peer Reviewed
• [Journal Article] Affability of equivalence relations arising from two-dimensional substitution tilings (2006)
  • Author(s): H. Matui
  • Journal Title: Ergodic Theory Dynam. Systems 26 Pages: 467-480
  • Peer Reviewed
• [Journal Article] Affability of equivalence relations arising from two-dimensional substitution tilings (2006)
  • Author(s): Hiroki Matui
  • Journal Title: Ergodic Theory and Dynamical Systems 26, No. 2 Pages: 467-480
• [Journal Article] Minimal dynamical systems on the product of the Cantor set and the circle II (2006)
  • Author(s): Huaxin Lin, Hiroki Matui
  • Journal Title: Selecta Mathematica 12, No. 2 Pages: 199-239
• [Journal Article] Torsion in coinvariants of certain Cantor minimal Z^2-systems
  • Author(s): H. Matui
  • Journal Title: Transactions of the American Mathematical Society 発表予定
  • Peer Reviewed
• [Journal Article] Orbit equivalence for Cantor minial Z^2-systems
  • Author(s): T. Giordano, H. Matui, I.F. Putnam and C.F. Skau
  • Journal Title: Journal of the American Mathematical Society 発表予定
  • Peer Reviewed
• [Journal Article] The absorption theorem for affable equivalence relations
  • Author(s): T. Giordano, H. Matui, I.F. Putnam and C.F. Skau
  • Journal Title: Ergodic Theory and Dynamical Systems 発表予定
  • Peer Reviewed
• [Journal Article] Classification of uniformly outer actions of Z^2 on UHF algebras
  • Author(s): T. Katsura and H. Matui
  • Journal Title: Advances in Mathematics 発表予定
  • Peer Reviewed
• [Journal Article] A short proof of affability for certain Cantor minimal Z^2-systems
  • Author(s): Hiroki Matui
  • Journal Title: Canadian Mathematical Bulletin (未定)
• [Presentation] C*環のK理論とKK理論 (2008)
  • Author(s): 松井宏樹
  • Organizer: 空間の代数的・幾何的モデルとその周辺
  • Place of Presentation: 信州大学
  • Year and Date: 2008-09-12
• [Presentation] カントール極小系の軌道同型による分類 (2008)
  • Author(s): 松井宏樹
  • Organizer: 日本数学会年会特別講演
  • Place of Presentation: 近畿大学
  • Year and Date: 2008-03-24
• [Presentation] Z^2-actions on UHF algebras (2007)
  • Author(s): Hiroki Matui
  • Organizer: Workshop on Structure of C*-Algebras
  • Place of Presentation: Fields Institute
  • Year and Date: 2007-11-16
• [Presentation] Z^2-actions on UHF algebras (2007)
  • Author(s): H. Matui
  • Organizer: Workshop on Structure of C*-Algebras
  • Place of Presentation: Fields Institute (Toronto)
  • Year and Date: 2007-11-16
• [Presentation] Cantor minimal Z^d systems and C*-algebras (2007)
  • Author(s): Hiroki Matui
  • Organizer: Operator Algebras and Related Fields(Combined Japan-US and West Coast Operator Algebra Seminar)
  • Place of Presentation: ハワイ大学
  • Year and Date: 2007-01-29
• [Presentation] カントール極小Z^2系の軌道同型による分類について (2007)
  • Author(s): 松井宏樹
  • Organizer: タイリング-準周期性の数理
  • Place of Presentation: 慶応大学
  • Year and Date: 2007-01-23
• [Presentation] カントール極小Z^2系の軌道同型による分類について (2006)
  • Author(s): 松井宏樹
  • Organizer: 日本数学会秋季総合分科会一般講演
  • Place of Presentation: 大阪市立大学
  • Year and Date: 2006-09-21
• [Presentation] カントール極小Z^2系の軌道同型による分類について (2006)
  • Author(s): 松井宏樹
  • Organizer: 共同研究・作用素環論の発展
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2006-09-07