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Research on algebraic properties of categories of modules and structures of Frobenius algebras

Research Project

Project/Area Number 19540014
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionTokyo University of Agriculture and Technology

Principal Investigator

YAMAGATA Kunio  Tokyo University of Agriculture and Technology, 大学院・共生科学技術研究院, 教授 (60015849)

Co-Investigator(Kenkyū-buntansha) YOSHINO Yuji  岡山大学, 大学院・自然科学研究科, 教授 (00135302)
和田 倶幸  東京農工大学, 大学院・共生科学技術研究院, 教授 (30134795)
浅芝 秀人  静岡大学, 理学部, 教授 (70175165)
Co-Investigator(Renkei-kenkyūsha) WADA Tomoyuki  東京農工大学, 大学院・共生科学研究院, 教授 (30134795)
ASASHIBA Hideto  静岡大学, 理学部, 教授 (70175165)
Project Period (FY) 2007 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2007: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Keywords環 / 多元環 / 加群 / 表現 / 圏 / クイバー / 有限次元多元環 / Frobenius多元環 / 入射加群 / 準同型環 / 部分圏
Research Abstract

多元環の構造とその上の加群の成す圏について研究を行い、加群の直既約部分加群の直和分解と加群の準同型環との関係や、Cohen-Macaulay加群の分類、有限次元群多元環のFrobenius多元環としてのカルタン行列の持つ性質、加群圏の被覆理論の拡張と応用などについて多くの成果を上げた。これらの諸成果は本研究組織の各研究者によって国内外の国際研究集会やシンポジウムなどで発表され専門雑誌に掲載された

Report

(3 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • Research Products

    (36 results)

All 2009 2008 2007

All Journal Article (16 results) (of which Peer Reviewed: 15 results) Presentation (20 results)

  • [Journal Article] Local Cohomology based on a nonclosed support defined by a pair of ideals2009

    • Author(s)
      R. Takahashi, Y. Yoshino, and T. Yoshizawa
    • Journal Title

      J. Pure and Appl. Algebra vol.213

      Pages: 582-600

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Ext-indices of ring extensions2009

    • Author(s)
      S. Nasseh, Y. Yoshino
    • Journal Title

      J. Pure and Applied Algebra vol.213

      Pages: 1216-1223

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Ext-indices of ring extensions2009

    • Author(s)
      Saeed Nasseh
    • Journal Title

      Journal of Pure and Applied Algebra 213

      Pages: 1216-1223

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Local cohomology based on a nonclosed support defined bya pair of ideals2009

    • Author(s)
      Ryo Takahashi
    • Journal Title

      Journal of Pure and Applied Algebra 213

      Pages: 582-600

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Modules with semiregular endomorphism rings2008

    • Author(s)
      K. Yamagata
    • Journal Title

      Colloquium Mathematicum vol.113

      Pages: 241-250

    • Related Report
      2008 Final Research Report
  • [Journal Article] Cartan matrices of symmetric algebras having generalized standard stable tubes2008

    • Author(s)
      J. Bialkowski, A. Skowronski, and K. Yamagata
    • Journal Title

      Osaka Journal of Mathematics vol.45

      Pages: 159-171

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Selfinjective algebras of quasitilted type2008

    • Author(s)
      A. Skowronski, and K. Yamagata
    • Journal Title

      Trends in representation theory of algebras and related topics

      Pages: 639-708

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Mutations in triangulated categories and rigid Cohen-Macaulay modules2008

    • Author(s)
      Osamu Iyama, and Y. Yoshino
    • Journal Title

      Inventiones Matematicae vol.172

      Pages: 117-168

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Universal lifts of chain complexes over non-commutative parameter algebras2008

    • Author(s)
      Y. Yoshino
    • Journal Title

      J. of Math of Kyoto Univ vol.48

      Pages: 793-845

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Eigenvalues of Cartan matrices of principal 2-blocks with abelian defect groups2008

    • Author(s)
      N. Kunugi, and T. Wada
    • Journal Title

      J. Algebra vol.319

      Pages: 4404-4411

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Domestic canonical algebras and simple Lie algebras2008

    • Author(s)
      H. Asashiba
    • Journal Title

      Math.Z vol.259

      Pages: 713-754

    • NAID

      120001794399

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Selfinjective algebras of quasiti1ted type2008

    • Author(s)
      Andrzej Skowronski
    • Journal Title

      Trends in representation theory ofalgebras and related topi cs (単行本)

      Pages: 639-708

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Mutations in triangulated categories and rigid Cohen-Macaulaymodules2008

    • Author(s)
      Osamu Iyama
    • Journal Title

      Inventiones Matematicae 172

      Pages: 117-168

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Universal lifts of chain complexes over non-commutativeparameter algebras2008

    • Author(s)
      Yuji Yoshino
    • Journal Title

      Journal of Mathematics of Kyoto University 48

      Pages: 793-845

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Eigenvalues of Cartan matrices of principal 2-blocks withabelian defect groups2008

    • Author(s)
      Naoko Kunugi
    • Journal Title

      Journal of Algebra 319

      Pages: 4404-4411

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cartan matrices of symmetric algebras having generalized standard stable tubes2008

    • Author(s)
      Jezy Bialkowski
    • Journal Title

      Osaka Journal of Mathematics 45

      Pages: 159-171

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Auto-equivalences of additivefull subcategories2009

    • Author(s)
      吉野雄二
    • Organizer
      第4回日本-ベトナム合同セミナー
    • Place of Presentation
      明治大学(生田)
    • Related Report
      2008 Final Research Report
  • [Presentation] フロベニウスの右作用と左作用2009

    • Author(s)
      吉野雄二
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京大学(駒場)
    • Related Report
      2008 Annual Research Report
  • [Presentation] 加法的部分圏の自己同型群2009

    • Author(s)
      吉野雄二
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京大学(駒場)
    • Related Report
      2008 Annual Research Report
  • [Presentation] 射影次元が有限な加群への埋め込み2009

    • Author(s)
      吉野雄二
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京大学(駒場)
    • Related Report
      2008 Annual Research Report
  • [Presentation] Auto-equivalences of additive full subcategories2009

    • Author(s)
      吉野雄二
    • Organizer
      The 4^<th> Japan-Vietnam Joint Seminar
    • Place of Presentation
      明治大学(生田)
    • Related Report
      2008 Annual Research Report
  • [Presentation] Eigenvalues of Cartan matrices of principal 2-blocks with abelian defect groups2008

    • Author(s)
      和田倶幸
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Related Report
      2008 Final Research Report
  • [Presentation] Eigenvalues of Cartan matrices of principal 2-blocks withabelian defect groups2008

    • Author(s)
      和田倶幸
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Related Report
      2008 Annual Research Report
  • [Presentation] Skew monoid categories and derived equivalences2008

    • Author(s)
      浅芝秀人
    • Organizer
      XIII International Conference on Representations of Algebras
    • Place of Presentation
      Sao Paulo, Brazil
    • Year and Date
      2008-08-08
    • Related Report
      2008 Final Research Report
  • [Presentation] Skew monoid categories and derived equivalences2008

    • Author(s)
      浅芝秀人
    • Organizer
      xIll Iinternational Conference onRepresentations of Algebras
    • Place of Presentation
      Sao Paulo (Brazil)
    • Year and Date
      2008-08-08
    • Related Report
      2008 Annual Research Report
  • [Presentation] Eigenvalues of Cartan matrices of principal 2-blocks withabelian defect groups2008

    • Author(s)
      和田倶幸
    • Organizer
      第25会代数的組み合わせ論シンポジウム
    • Place of Presentation
      北海道大学
    • Year and Date
      2008-06-24
    • Related Report
      2008 Annual Research Report
  • [Presentation] Oicard groups and automorphism groups of categories2008

    • Author(s)
      吉野雄二
    • Organizer
      第41回環論および表現論シンポジウム
    • Place of Presentation
      静岡大学
    • Related Report
      2008 Final Research Report
  • [Presentation] Deforming a chain complexes to non-commutative direction2008

    • Author(s)
      吉野雄二
    • Organizer
      International Conference toward establishing a cutting-edge platform for commutative ring theory in the 21st century
    • Related Report
      2008 Final Research Report
  • [Presentation] Picard groups of additive full subcategories2008

    • Author(s)
      吉野雄二
    • Organizer
      第41回環論および表現論シンポジウム
    • Place of Presentation
      静岡大学
    • Related Report
      2008 Annual Research Report
  • [Presentation] Picard groups and automorphism groups of categories2008

    • Author(s)
      吉野雄二
    • Organizer
      第30回可換環論シンポジウム
    • Place of Presentation
      虹の松原ホテル(唐津市)
    • Related Report
      2008 Annual Research Report
  • [Presentation] Left versus right action of Frobenius2008

    • Author(s)
      吉野雄二
    • Organizer
      第30回可換環論シンポジウム
    • Place of Presentation
      虹の松原ホテル(唐津市)
    • Related Report
      2008 Annual Research Report
  • [Presentation] On lifting of idempotents in the endomorphism ring of a module2007

    • Author(s)
      山形邦夫
    • Organizer
      第5回日中韓「環論」国際シンポジウム
    • Place of Presentation
      国立オリンピック記念青少年総合センター(東京)
    • Year and Date
      2007-09-11
    • Related Report
      2008 Final Research Report
  • [Presentation] On lifting of idempotents in the endomorphism ring of a module2007

    • Author(s)
      Kunio Yamagata
    • Organizer
      The 5th Chaina-Japan-Korea International Symposium on Ring Theory
    • Place of Presentation
      国立オリンピック記念青少年総合センター
    • Year and Date
      2007-09-11
    • Related Report
      2007 Annual Research Report
  • [Presentation] Covering functors, orbit categories and derived equivalences2007

    • Author(s)
      浅芝秀人
    • Organizer
      XII International Conference on Representations of Algebras
    • Place of Presentation
      Nicolaus Copernicus University, Poland
    • Year and Date
      2007-08-23
    • Related Report
      2008 Final Research Report
  • [Presentation] Covering functors, orbit categories and derived equivalences2007

    • Author(s)
      Hideto Asashiba
    • Organizer
      The XIIth international Conference on Representations of Algebras
    • Place of Presentation
      コペルニクス大学(ポーランド)
    • Year and Date
      2007-08-23
    • Related Report
      2007 Annual Research Report
  • [Presentation] 非可換パラメーターを基準にした鎖複体の普遍持ち上げ2007

    • Author(s)
      吉野雄二
    • Organizer
      第52回代数学シンポジウム
    • Place of Presentation
      神戸大学
    • Year and Date
      2007-08-09
    • Related Report
      2008 Final Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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