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Classification theory of C*-algebras over finite spaces

Research Project

Project/Area Number 24740109
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Global analysis
Research InstitutionKeio University

Principal Investigator

KATSURA Takeshi  慶應義塾大学, 理工学部(矢上), 准教授 (50513298)

Project Period (FY) 2012-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords数学 / 関数解析 / 作用素環 / 分類 / 国際情報交換 / カナダ:デンマーク / 国際研究者交流 / アメリカ:カナダ:デンマーク
Outline of Final Research Achievements

In this research, we got not only various results on C*-algebras over finite spaces as expected, but also wide results on classification theory of C*-algebras. The results on C*-algebras over finite spaces include the one on K-theoretical invariants of Cuntz-Krieger algebras with the application to the conjecture of characterization of graph algebras, the complete solution to realization problem of K-theoretical invariants of non-simple graph algebras, and the result of determining which AF-algebras arise as non-simple graph algebras. The results on classification theory of C*-algebras include the ones on non-separable C*-algebras and on C*-algebras associated with discrete groups.

Report

(6 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (20 results)

All 2017 2016 2015 2014 2013 Other

All Int'l Joint Research (5 results) Journal Article (7 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 7 results,  Acknowledgement Compliant: 1 results) Presentation (6 results) (of which Invited: 5 results) Remarks (2 results)

  • [Int'l Joint Research] ヒューストン大学(米国)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] コペンハーゲン大学(デンマーク)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] ヒューストン大学(米国)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] ヨーク大学(カナダ)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] コペンハーゲン大学(デンマーク)

    • Related Report
      2015 Research-status Report
  • [Journal Article] The ranges of K-theoretic invariants for nonsimple graph algebras2016

    • Author(s)
      Eilers, Soren; Katsura, Takeshi; Tomforde, Mark; West, James
    • Journal Title

      Transactions of the American Mathematical Society

      Volume: 368 Pages: 3811-3847

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Nonseparable UHF algebras II: Classification2015

    • Author(s)
      Farah, Ilijas; Katsura, Takeshi
    • Journal Title

      Mathematica Scandinavica

      Volume: 117 Pages: 105-125

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the invariant uniform Roe algebra2014

    • Author(s)
      Katsura, Takeshi; Uuye, Otgonbayar
    • Journal Title

      The Journal of Operator Theory

      Volume: 72 Pages: 549-556

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Identifying AF-algebras that are graph C*-algebras2014

    • Author(s)
      Eilers, Soren; Katsura, Takeshi; Ruiz, Efren; Tomforde, Mark
    • Journal Title

      J. Funct. Anal

      Volume: 266 Pages: 3968-3996

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] The K-theoretical range of Cuntz-Krieger algebras2014

    • Author(s)
      Arklint, Sara E.; Bentmann, Rasmus; Katsura, Takeshi
    • Journal Title

      J. Funct. Anal

      Volume: 266 Pages: 5448-5466

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Dynamical systems of type (m,n) and their C*-algebras.2013

    • Author(s)
      Ara, Pere; Exel, Ruy; Katsura, Takeshi
    • Journal Title

      Ergodic Theory Dynam. Systems

      Volume: 33 Pages: 1291-1325

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Dynamical systems of type (m,n) and their C*-algebras2013

    • Author(s)
      Pere Ara, Ruy Exel, Takeshi Katsura
    • Journal Title

      Ergodic Theory and Dynamical Systems

      Volume: To appear

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] On magic square C*-algebras2017

    • Author(s)
      勝良健史
    • Organizer
      Kyoto Operator Algebra Seminar
    • Place of Presentation
      京都大学(京都府・京都市)
    • Year and Date
      2017-03-08
    • Related Report
      2016 Annual Research Report
  • [Presentation] Warped crossed products and their applications2016

    • Author(s)
      勝良健史
    • Organizer
      作用素環論の最近の進展
    • Place of Presentation
      数理解析研究所(京都府・京都市)
    • Year and Date
      2016-09-12
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Classification of C*-algebras with finitely many ideals

    • Author(s)
      Takeshi Katsura
    • Organizer
      Workshop on Operator Algebras
    • Place of Presentation
      University of Tokyo
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Classification of purely infinite C*-algebras with finitely many ideals

    • Author(s)
      勝良健史
    • Organizer
      GPOTS 2012
    • Place of Presentation
      the University of Houston
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Problems on non-simple semiprojective C*-algebras

    • Author(s)
      勝良健史
    • Organizer
      Workshop on Semiprojective C*-Algebras
    • Place of Presentation
      University of Copenhagen
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Characterization of Cuntz-Krieger algebras

    • Author(s)
      勝良健史
    • Organizer
      作用素論・作用素環論研究集会
    • Place of Presentation
      大阪教育大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Remarks] Papers of Takeshi Katsura

    • URL

      http://www.math.keio.ac.jp/~katsura/papers/index.html

    • Related Report
      2016 Annual Research Report
  • [Remarks] Papers of Takeshi Katsura

    • URL

      http://www.math.keio.ac.jp/~katsura/papers/index.html

    • Related Report
      2012 Research-status Report

URL: 

Published: 2013-05-31   Modified: 2022-02-16  

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