Structure of operator algebras and its applications to Classification of symbolic dynamical systems

• Project/Area Number: 20540215
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Yokohama City University
• Principal Investigator: MATSUMOTO Kengo Yokohama City University, 大学院・学校教育研究科, 教授 (40241864)
• Co-Investigator(Renkei-kenkyūsha): TOMIYAMA Jun 東京都立大学, 理学部, 名誉教授 (30006928)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000); Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 作用素環 / C*-環 / 記号力学系 / サブシフト / 軌道同型 / 位相的マルコフシフト

Research Abstract

I have studied mainly orbit equivalence of symbolic dynamical systems and related C^*-algebras. The results have been published in three papers. Especially, it has been proved that the continuous orbit equivalence classes of one-sided topological Markov shifts exactly correspond to the isomorphism classes of the associated Cuntz-Krieger algebras keeping their Cartan subalgebras. I also studied simplicity condition and several examples of C^*-algebras defined by C^*-symbolic dynamical systems. K-theory groups for C^*-algebras associated with concrete non sofic subshifts have been studied. I have began to study KMS condition for C^*-symbolic dynamical systems for which inverse temperatures are not necessarily real numbers.

Research Products

• [Journal Article] A class of simple $C^*$-algebras arising from certain nonsofic subshifts (2011)
  • Author(s): 松本健吾
  • Journal Title: Ergodic Theory and Dynamical Systems 31巻 Pages: 459-482
  • Peer Reviewed
• [Journal Article] A class of simple C^*-algebras arising from certain non sofic subshifts (2011)
  • Author(s): Kengo Matsumoto
  • Journal Title: Ergodic Theory and Dynamical systems Volume: 31 Pages: 459-482
  • Peer Reviewed
• [Journal Article] Orbit equivalence of one-sided subshifts and the associated C*-algebras (2010)
  • Author(s): 松本健吾
  • Journal Title: Yokohama Mathematical Journal 56巻 Pages: 59-85
  • NAID: 120006360248
  • Peer Reviewed
• [Journal Article] Orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras (2010)
  • Author(s): 松本健吾
  • Journal Title: Pasific Journal of Mathematics 246巻 Pages: 199-255
  • Peer Reviewed
• [Journal Article] Actions of symbolic dynamical systems on C*-algebras II.Simplicity of C*-symbolic crossed products and some examples (2010)
  • Author(s): 松本健吾
  • Journal Title: Mathematische Zeitshrift 265巻 Pages: 735-760
  • Peer Reviewed
• [Journal Article] Orbit equivalence of one-sided subshifts and the associated C^*-algebras (2010)
  • Author(s): Kengo Matsumoto
  • Journal Title: Yokohama Mathematical Journal Volume: 56 Pages: 59-85
  • NAID: 120006360248
  • Peer Reviewed
• [Journal Article] Orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras (2010)
  • Author(s): Kengo Matsumoto
  • Journal Title: Pacific journal of Mathematics Volume: 246 Pages: 199-225
  • Peer Reviewed
• [Journal Article] Actions of symbolic dynamical systems on C^*-algebras, II Simplicity of C^*-symbolic crossed products and some examples (2010)
  • Author(s): Kengo Matsumoto
  • Journal Title: Mathematiche Zetschrift Volume: 265 Pages: 735-760
  • Peer Reviewed
• [Journal Article] Classification of ideals homeomorphism c*-algebras and quasidiagonality (2009)
  • Author(s): 富山淳
  • Journal Title: Acta applicable Mathematics 108巻 Pages: 561-572
• [Journal Article] On the commutant of C(X) in C*-crossed products by Z (2009)
  • Author(s): Svensson Christa, 富山淳
  • Journal Title: Journal of Functional Analysis 256巻 Pages: 2367-2386
• [Journal Article] Orbit equivalence in C*-algebras defined by actions of symbolic dynamical systems (2009)
  • Author(s): 松本健吾
  • Journal Title: Contemporary Mathematics 503巻 Pages: 121-140
  • Peer Reviewed
• [Journal Article] Subshifts and C*-algebras from one-counter codes (2009)
  • Author(s): Wolfgang Krieger, 松本健吾
  • Journal Title: Contemporary Mathematics 503巻 Pages: 93-119
  • Peer Reviewed
• [Journal Article] Cuntz-krieger環の生成元達の組み合わせ論的性質と関連する力学系のゼータ関数について (2009)
  • Author(s): 松本健吾
  • Journal Title: 数理解析研究所講究録 1627 Pages: 18-49
  • NAID: 110007016668
• [Journal Article] Textile systems on lambda-graph systems (2008)
  • Author(s): 松本健吾
  • Journal Title: Yokohama Mathematical Journal 54巻 Pages: 161-206
  • NAID: 120006459878
  • Peer Reviewed
• [Journal Article] Textile systems on lambda grapli systems (2008)
  • Author(s): Kengo Matsamoto
  • Journal Title: Yokohama Mathermatical Journal 54 Pages: 161-206
  • Peer Reviewed
• [Journal Article] A class of simple C^*-algebras arising from certain nonsofic subshifts
  • Author(s): Kengo Matsumoto
  • Journal Title: Ergodic Theory and Dynamical System (印刷中)
  • Peer Reviewed
• [Journal Article] Orbit equivalence of one-sided subshifts and the associated C^*-algebras
  • Author(s): Kengo Matsumoto
  • Journal Title: Yokohama Mathematical Journal (印刷中)
  • NAID: 120006360248
  • Peer Reviewed
• [Presentation] タイルばりの作用からできるC*-環について (2010)
  • Author(s): 松本健吾
  • Organizer: 日本数学会
  • Place of Presentation: 早稲田大学
  • Year and Date: 2010-03-22
• [Presentation] C*-力学系のJordan標準形とKMS条件 (2009)
  • Author(s): 松本健吾
  • Organizer: 日本数学会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-25
• [Presentation] The C*-algebras of onecounter codes and flow equivalence (2009)
  • Author(s): 松本健吾
  • Organizer: 日本数学会
  • Place of Presentation: 東京大学駒場
  • Year and Date: 2009-03-28
• [Presentation] Subshifts from one-counter codes (2009)
  • Author(s): 松本健吾-W. knger
  • Organizer: 日本数学会
  • Place of Presentation: 東京大学(駒場)
  • Year and Date: 2009-03-25
• [Book] Applications of infinite labeled graphs to symbolic dynamical systems, Structural Analysis and Complex Networks(M.Dehmer 編,共著) (2010)
  • Author(s): 松本健吾
  • Publisher: Springer
• [Remarks] ホームページ等
  • URL: http://www.juen.ac.jp//math/matsumoto/matsumoto.html