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2013 Fiscal Year Final Research Report

Auslander-Reiten quivers of group rings

Research Project

  • PDF
Project/Area Number 23540054
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionOsaka City University

Principal Investigator

KAWATA Shigeto  大阪市立大学, 大学院理学研究科, 准教授 (50195103)

Co-Investigator(Renkei-kenkyūsha) KANEDA Masaharu  大阪市立大学, 大学院・理学研究科, 教授 (60204575)
BABA Yoshitomo  大阪教育大学, 教育学部, 教授 (10201724)
Project Period (FY) 2011 – 2013
KeywordsAuslander-Reiten有向グラフ / 有限群の表現 / 概分裂列
Research Abstract

Let RG be an integral group ring of a finite group G over a complete discrete valuation ring R with residue class field k of positive characteristic. Suppose that L is an indecomposable RG-lattice of height zero, and let S be a source of L. We have shown that the tree class of the Auslander-Reiten component containing L is A-infinity if and only if the tree class of the Auslander-Reiten component containing S is A-infinity. Also, we have proved that the middle term of the almost split sequence terminating in L is indecomposable if the reduced kG-module of L is indecomposable. In the case of 2-modular system, we have shown that the tree classes of the Auslander-Reiten components containing odd rank RG-lattices are A-infinity.

  • Research Products

    (4 results)

All 2014 2013 2012 2011

All Journal Article (2 results) (of which Peer Reviewed: 1 results) Presentation (2 results)

  • [Journal Article] 群環の高さ0 の表現加群とAuslander-Reiten 連結成分について2014

    • Author(s)
      河田成人
    • Journal Title

      数理解析研究所講究録1872巻「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」

      Pages: 140-150

  • [Journal Article] On Auslander-Reiten components and splitting trace lattices for integral group rings2012

    • Author(s)
      Shigeto Kawata
    • Journal Title

      Journal of Algebra

      Volume: vol.359 Pages: 69-79

    • Peer Reviewed
  • [Presentation] 群環の高さ0の表現加群とAuslander-Reiten連結成分について2013

    • Author(s)
      河田成人
    • 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
    • Year and Date
      2013-01-09
  • [Presentation] 群環のAuslander-Reiten 成分とテンサー積について2011

    • Author(s)
      河田成人
    • Organizer
      2011年度日本数学会秋期総合分科会
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-28

URL: 

Published: 2015-07-16  

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