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曲面上の組合せ論のブラウアーグラフ多元環を用いた圏化

Research Project

Project/Area Number 17J05537
Research Category

Grant-in-Aid for JSPS Fellows

Allocation TypeSingle-year Grants
Section国内
Research Field Algebra
Research InstitutionYamaguchi University (2019)
Osaka Prefecture University (2017-2018)

Principal Investigator

足立 崇英  山口大学, 国際総合科学部, 助教

Project Period (FY) 2017-04-26 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords傾対象 / ブラウアーグラフ多元環 / 傾理論 / リボングラフ / 対称多元環
Outline of Annual Research Achievements

本研究の目的は、ブラウアーグラフ多元環の傾対象の組合せ的分類を与えることであった。前年度までにブラウアーグラフ多元環とアークシステムを持つ装飾点付曲面との関係を明らかにし、前傾複体と呼ばれる傾複体よりも弱い概念と曲面上の「非交差」な曲線の集合の間の対応を得た。該当年度の目標は、この対応を強めて、傾対象の曲面上の組合せ的解釈を与えることであった。残念ながらこの目標を達成することはできなかった。

Research Progress Status

令和元年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

令和元年度が最終年度であるため、記入しない。

Report

(3 results)
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • Research Products

    (9 results)

All 2019 2018 2017

All Journal Article (4 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 2 results,  Open Access: 1 results) Presentation (5 results)

  • [Journal Article] A geometric model of Brauer graph algebras2019

    • Author(s)
      Takahide Adachi, Aaron Chan
    • Journal Title

      Proceedings of the 51st Symposium on Ring Theory and Representation Theory

      Volume: 1 Pages: 1-5

    • Related Report
      2018 Annual Research Report
  • [Journal Article] Discreteness of silting objects and t-structures in triangulated categories2018

    • Author(s)
      Adachi Takahide、Mizuno Yuya、Yang Dong
    • Journal Title

      Proceedings of the London Mathematical Society

      Volume: 118 Issue: 1 Pages: 1-42

    • DOI

      10.1112/plms.12176

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] How to capture t-structures by silting theory2018

    • Author(s)
      Takahide Adachi、Yuya Mizuno
    • Journal Title

      Proceedings of the 50th Symposium on Ring Theory and Representation Theory

      Volume: 1

    • Related Report
      2017 Annual Research Report
  • [Journal Article] Classification of two-term tilting complexes over Brauer graph algebras2017

    • Author(s)
      Adachi Takahide、Aihara Takuma、Chan Aaron
    • Journal Title

      Mathematische Zeitschrift

      Volume: 印刷中 Issue: 1-2 Pages: 1-36

    • DOI

      10.1007/s00209-017-2006-9

    • Related Report
      2018 Annual Research Report 2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] Silting objects and t-structures2018

    • Author(s)
      Takahide Adachi
    • Organizer
      Higher homological algebra and cluster tilting
    • Related Report
      2018 Annual Research Report
  • [Presentation] Silting objects and t-structures2018

    • Author(s)
      Takahide Adachi
    • Organizer
      ICRA 2018
    • Related Report
      2018 Annual Research Report
  • [Presentation] A geometric model of Brauer graph algebras2018

    • Author(s)
      Takahide Adachi
    • Organizer
      第51回環論および表現論シンポジウム
    • Related Report
      2018 Annual Research Report
  • [Presentation] Silting objects and t-structures2017

    • Author(s)
      Takahide Adachi
    • Organizer
      Conference on Algebraic Representation Theory
    • Related Report
      2017 Annual Research Report
  • [Presentation] How to capture t-structures by silting theory2017

    • Author(s)
      Takahide Adachi
    • Organizer
      第50回環論および表現論シンポジウム
    • Related Report
      2017 Annual Research Report

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Published: 2017-05-25   Modified: 2024-03-26  

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