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Research on finite dimensional algebras of finite global dimension using rejective chains

Research Project

Project/Area Number 19K14513
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 11010:Algebra-related
Research InstitutionYamaguchi University

Principal Investigator

Tsukamoto Mayu  山口大学, 大学院創成科学研究科, 講師 (40832910)

Project Period (FY) 2019-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2022: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords大域次元 / 準遺伝多元環 / 削除鎖 / 強準遺伝多元環 / Neat 多元環 / 準傾対象 / Extriangulated 圏 / Stratified 多元環
Outline of Research at the Start

本研究では, 削除鎖を用いて大域次元が有限な多元環を研究する. 最近, 特別な大域次元が有限な多元環 (強準遺伝環) と削除鎖との関係が明らかとなった. そこで本研究ではこの関係を足場とし, 大域次元が有限な自己準同型環の性質を削除鎖を用いて調べる. 具体的には自己準同型環を実現する加群に着目し, 大域次元が有限な自己準同型環の構成を与えることを目指す. また大域次元が 2 以下の場合に着目した研究も行う.

Outline of Final Research Achievements

I studied finite dimensional algebras of finite global dimension using categorical methods. I researched the relationship between neat algebras, which are finite dimensional algebras of finite global dimension, and sequences of subcategories called rejective chains. In joint work on Dlab--Ringel's standardization method, we obtained constructions of finite dimensional algebras including quasi-hereditary algebras, and also generalized and unified Dlab--Ringel's standardization method to extriangulated categories. Moreover, I conducted joint work on tilting modules and weak dominant dimension, and we gave a sufficient condition for relative Auslander algebras to be strongly quasi-hereditary algebras.

Academic Significance and Societal Importance of the Research Achievements

大域次元が有限な多元環は多元環の表現論において重要な研究対象の一つであり, リー理論や代数幾何学など関連分野にも現れる. 本研究では, 削除鎖をはじめとする圏論的な手法を用いて, 大域次元が有限な多元環の判定法について考察を行い, 大域次元が有限となるための十分条件を複数与えた. ここで得られた十分条件は比較的容易に確認できるため, 本研究の成果は大域次元が有限な多元環の研究に寄与があると思われる.

Report

(6 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • Research Products

    (18 results)

All 2024 2023 2022 2021 2019 2018

All Journal Article (6 results) (of which Peer Reviewed: 6 results) Presentation (12 results) (of which Int'l Joint Research: 1 results,  Invited: 5 results)

  • [Journal Article] Mixed standardization and Ringel duality2024

    • Author(s)
      Adachi Takahide、Tsukamoto Mayu
    • Journal Title

      Journal of Algebra

      Volume: 641 Pages: 546-586

    • DOI

      10.1016/j.jalgebra.2023.11.032

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Intervals of <i>s</i>-torsion pairs in extriangulated categories with negative first extensions2022

    • Author(s)
      ADACHI TAKAHIDE、ENOMOTO HARUHISA、TSUKAMOTO MAYU
    • Journal Title

      Mathematical Proceedings of the Cambridge Philosophical Society

      Volume: Online Issue: 3 Pages: 1-19

    • DOI

      10.1017/s0305004122000354

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Characterizations of right rejective chains2022

    • Author(s)
      Mayu Tsukamoto
    • Journal Title

      Canadian Mathematical Bulletin

      Volume: 65 Issue: 3 Pages: 557-570

    • DOI

      10.4153/s0008439521000540

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Hereditary cotorsion pairs and silting subcategories in extriangulated categories2022

    • Author(s)
      Adachi Takahide、Tsukamoto Mayu
    • Journal Title

      Journal of Algebra

      Volume: 594 Pages: 109-137

    • DOI

      10.1016/j.jalgebra.2021.11.029

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Tilting modules and dominant dimension with respect to injective modules2021

    • Author(s)
      Adachi Takahide、Tsukamoto Mayu
    • Journal Title

      The Quarterly Journal of Mathematics

      Volume: 72 Issue: 3 Pages: 855-884

    • DOI

      10.1093/qmath/haaa050

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Strongly quasi-hereditary algebras and rejective subcategories2018

    • Author(s)
      Mayu Tsukamoto
    • Journal Title

      Nagoya Mathematical Journal

      Volume: 印刷中 Pages: 10-38

    • DOI

      10.1017/nmj.2018.9

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Presentation] 混合階層化代数の構成2023

    • Author(s)
      塚本 真由
    • Organizer
      日本数学会2023年度秋季総合分科会
    • Related Report
      2023 Annual Research Report
  • [Presentation] A construction of quasi-hereditary algebras2023

    • Author(s)
      塚本 真由
    • Organizer
      パーシステントホモロジーと表現論
    • Related Report
      2022 Research-status Report
    • Invited
  • [Presentation] Cotorsion pairs and silting subcategories in extriangulated categories2022

    • Author(s)
      塚本 真由
    • Organizer
      吹田表現論セミナー
    • Related Report
      2022 Research-status Report
    • Invited
  • [Presentation] A bijection between silting subcategories and bounded hereditary cotorsion pairs2022

    • Author(s)
      塚本 真由
    • Organizer
      第54回環論および表現論シンポジウム
    • Related Report
      2022 Research-status Report
  • [Presentation] Extriangulated 圏の余ねじれ対と準傾部分圏2022

    • Author(s)
      塚本 真由
    • Organizer
      日本数学会2022年度秋季総合分科会
    • Related Report
      2022 Research-status Report
  • [Presentation] 準遺伝代数について2022

    • Author(s)
      塚本 真由
    • Organizer
      第5回岡潔女性数学者セミナー
    • Related Report
      2022 Research-status Report
    • Invited
  • [Presentation] 強準遺伝代数の圏論的特徴付けとその応用2022

    • Author(s)
      塚本真由
    • Organizer
      2021年度大阪市立大学数学研究会特別賞受賞講演
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] Intervals of s-torsion pairs in extriangulated categories with negative first extensions2021

    • Author(s)
      塚本真由
    • Organizer
      南大阪代数セミナー
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] Intervals of s-torsion pairs in extriangulated categories with negative first extensions2021

    • Author(s)
      塚本真由
    • Organizer
      第53回環論および表現論シンポジウム
    • Related Report
      2021 Research-status Report
  • [Presentation] Constructions of rejective chains2019

    • Author(s)
      Mayu Tsukamoto
    • Organizer
      The Eighth China-Japan-Korea International Symposium on Ring Theory
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Tilting modules and dominant dimension with respect to injective modules2019

    • Author(s)
      Mayu Tsukamoto
    • Organizer
      日本数学会 2019年度秋季総合分科会
    • Related Report
      2019 Research-status Report
  • [Presentation] 準遺伝代数について2019

    • Author(s)
      Mayu Tsukamoto
    • Organizer
      整数論・環論合同セミナー
    • Related Report
      2019 Research-status Report

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Published: 2019-04-18   Modified: 2025-01-30  

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