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2009 Fiscal Year Self-evaluation Report

Study on Complex dynamical systems and operator algebras

Research Project

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Project/Area Number 19340040
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionKyushu University

Principal Investigator

WATATANI Yasuo  Kyushu University, 大学院・数理学研究院, 教授 (00175077)

Project Period (FY) 2007 – 2010
Keywords作用素環 / 複素力学系 / C*-環
Research Abstract

(1)この研究では有理関数や超越整関数などの複素平面上の有理型関数Rの反復合成(R^n)_nによる複素力学系から、ヒルベルト空間上の作用素からなるC*-環を構成する。この研究の目的は複素力学系と作用素環という二つの異なった分野の思いもかけない結びつきを解明することである。
(2)2次以上の有理関数は位相同型写像ではないので、接合積でもって作用素環を構成することができない。そこでこれをリーマン球面上の有限被覆写像なので、分岐指数を使ってそのグラフ上の連続関数全体は係数環上の双加群になる。この双加群からCuntz Pimsner構成を使ってC*-環を対応させる。リーマン球面全体とJulia集合とFatou集合のそれぞれ上で考えることで、3つのC*-環を構成する。
(3)分岐点のような特異点の構造と付随するC*-環との関連を研究する。そのC*-環上のK理論やKMS状態(平衡状態)の言葉で、元の特異点の構造を記述することを目指す。

  • Research Products

    (11 results)

All 2009 2008 2007 Other

All Journal Article (6 results) Presentation (5 results)

  • [Journal Article] Indecomposable representations of quivers on infinite-dimensional Hilbert spaces2009

    • Author(s)
      M. Enomoto, Y. Watatani
    • Journal Title

      J.Funct.Anal. 256

      Pages: 959-991

  • [Journal Article] C*algebras associated with Mauldin-Williams graphs2008

    • Author(s)
      M. Ionescu, Y. Watatani
    • Journal Title

      Canad.Math.Bull. 51

      Pages: 545-560

  • [Journal Article] KMS states and branched points2007

    • Author(s)
      M. Izumi, T. Kajiwara, Y. Watatani
    • Journal Title

      Ergodic Th. & Dynam.Sys. 27

      Pages: 1887-1918

  • [Journal Article] Exotic indecomposable systems of four subspaces in a Hilbert space2007

    • Author(s)
      M. Enomoto, Y. Watatani
    • Journal Title

      Integr.Equ.and Oper.Theory 59

      Pages: 149-164

  • [Journal Article] Fundamental group of simple C*-algebras with unique trace

    • Author(s)
      N. Nawata, Y. Watatani
    • Journal Title

      Adv.Math. (to appear)

  • [Journal Article] Toeplitz composition C*-algebras for certain finite Blaschke products

    • Author(s)
      H. Hamada, Y. Watatani
    • Journal Title

      Proc.Amer.Math.Soc. (to appear)

  • [Presentation] Fundamental group of simple C*-algebras with unique trace2009

    • Author(s)
      Y. Watatani
    • Organizer
      University of Victoria
    • Place of Presentation
      Victoria, Canada
    • Year and Date
      20090700
  • [Presentation] Composition operators and C*-algebras associated with complex dynamical systems2009

    • Author(s)
      Y. Watatani
    • Organizer
      Asia Mathematical Conference 2009
    • Place of Presentation
      Kuala Lumpur, Malaysia
    • Year and Date
      20090600
  • [Presentation] Complex dynamical systems and associated C*-algebras2008

    • Author(s)
      Y. Watatani
    • Organizer
      Lorentz Center
    • Place of Presentation
      Leiden, Netherlands
    • Year and Date
      20080700
  • [Presentation] C*-algebras associated with algebraic correspondences2008

    • Author(s)
      Y. Watatani
    • Organizer
      Bunff International Research Station
    • Place of Presentation
      Bunff, Canada
    • Year and Date
      20080100
  • [Presentation] Branched points and C*-algebras associated with complex dynamical systems2007

    • Author(s)
      Y. Watatani
    • Organizer
      Hanyang University
    • Place of Presentation
      Seoul, Korea
    • Year and Date
      20070600

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Published: 2011-06-18   Modified: 2016-04-21  

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