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Representations of Frobenius algebras

Research Project

Project/Area Number 25400036
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionTokyo University of Agriculture and Technology

Principal Investigator

Yamagata Kunio  東京農工大学, 工学(系)研究科(研究院), 名誉教授 (60015849)

Co-Investigator(Renkei-kenkyūsha) KIYITA Masao  東京医科歯科大学, 教養部, 教授 (50214911)
Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords多元環 / 加群 / 表現 / 圏 / フロベニウス多元環 / 森田多元環 / 有限次元多元環 / カルタン行列 / 国際研究者交流 / ポーランド / 森田不変 / ドイツ:中国
Outline of Final Research Achievements

We studied Frobenius algebras and Morita algebras, giving applications of them. One of the main results is a characterization of Frobenius algebras with some section in the AR quiver, and the other is a characterization for the endomorphism algebras of generators to be Morita algebras, which clarifies a relation between Morita algebras and hygher Auslander algebras. We described the Cartan matrices of blocks of some group algebras by using the dimensions of simple modules.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (16 results)

All 2016 2015 2014 2013 Other

All Int'l Joint Research (3 results) Journal Article (2 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 2 results,  Acknowledgement Compliant: 2 results) Presentation (11 results) (of which Int'l Joint Research: 1 results,  Invited: 8 results)

  • [Int'l Joint Research] コペルニクス大学(ポーランド)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] ハインリッヒ・ハイネ大学(ドイツ)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] 中国科学院数学与系統科学研究院(中国)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Morita endomorphism algebras of generators2016

    • Author(s)
      Otto Kerner, Kunio Yamagata
    • Journal Title

      Algebras and Representation Theory

      Volume: ー Issue: 3 Pages: 749-759

    • DOI

      10.1007/s10468-016-9601-z

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] On selfinjective algebras of tilted type2015

    • Author(s)
      Andrzej Skowronski, Kunio Yamagata
    • Journal Title

      Colloquium Mathematicum

      Volume: 印刷中

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] 剛性加群による有限次元多元環の軌道多元環構造判定定理2016

    • Author(s)
      山形邦夫
    • Organizer
      岡山大学代数セミナー
    • Place of Presentation
      岡山大学(岡山市北区津島中)
    • Year and Date
      2016-03-04
    • Related Report
      2015 Annual Research Report
  • [Presentation] Canonical bimodules of Morita algebras2015

    • Author(s)
      山形邦夫
    • Organizer
      メキシコ国立自治大学表現論セミナー
    • Place of Presentation
      メキシコ国立自治大学(メキシコシティー、メキシコ)
    • Year and Date
      2015-10-05
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Criterion theorems for a self-injective algebras to be an orbit algebra2015

    • Author(s)
      山形邦夫
    • Organizer
      北京首都師範大学多元環表現論セミナー
    • Place of Presentation
      北京首都師範大学(北京、中国)
    • Year and Date
      2015-09-10
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Orbit algebras of repetitive algebras2015

    • Author(s)
      山形邦夫
    • Organizer
      中国科学院数学与系統科学研究院代数セミナー
    • Place of Presentation
      中国科学院数学与系統科学研究院(北京、中国)
    • Year and Date
      2015-09-07
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Orbit algebras of repetitive algebras2015

    • Author(s)
      山形邦夫
    • Organizer
      北京師範大学多元環表現論セミナー
    • Place of Presentation
      北京師範大学(北京、中国)
    • Year and Date
      2015-09-02
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] On Morita algebras and Auslander algebras2015

    • Author(s)
      山形邦夫
    • Organizer
      4th Advances in Representation Theory of Algebras
    • Place of Presentation
      数学研究センター(グアナファト、メキシコ)
    • Year and Date
      2015-06-23
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On Cartan matrices determined by the dimensions of simple modules2015

    • Author(s)
      清田正夫
    • Organizer
      有限群のコホモロジー論とその周辺
    • Place of Presentation
      京都大学数理解析研究所(京都府京都市左京区北白川追分町)
    • Year and Date
      2015-02-18
    • Related Report
      2014 Research-status Report
  • [Presentation] 森田多元環について2014

    • Author(s)
      山形邦夫
    • Organizer
      可換環論と表現論
    • Place of Presentation
      岡山大学理学部(岡山県岡山市北区津島中)
    • Year and Date
      2014-10-11
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Morita algebras and their historical background2014

    • Author(s)
      山形邦夫
    • Organizer
      代数高等セミナー
    • Place of Presentation
      シュツットガルト大学(ドイツ、シュツットガルト)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] On Cartan matrices with two parameters2014

    • Author(s)
      清田正夫
    • Organizer
      RIMS研究集会 有限群とその表現・頂点作用素代数・代数的組合せ論の研究
    • Place of Presentation
      京都大学数理解析研究所(京都府京都市左京区)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 竹田の不等式について2013

    • Author(s)
      清田正夫
    • Organizer
      第25回有限群論草津セミナー
    • Place of Presentation
      草津セミナーハウス(群馬県吾妻郡草津町)
    • Related Report
      2013 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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