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2011 Fiscal Year Final Research Report

Representation theory of orders

Research Project

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Project/Area Number 21740010
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionNagoya University

Principal Investigator

IYAMA Osamu  名古屋大学, 多元数理科学研究科, 教授 (70347532)

Project Period (FY) 2009 – 2011
Keywords高次元Auslander-Reiten理論 / 箙(クイバー) / Cohen-Macaulay加群 / 団(クラスター)傾部分圏 / n有限表現型 / 団(クラスター)圏 / Calabi-Yau三角圏 / 導来圏 / 傾理論 / 変異 / 準傾対象 / 非可換特異点解消 / 団(クラスター)代数
Research Abstract

Studied higher dimensional Auslander-Reiten theory. My results were published in16 papers(11 papers were refereed). I gave 51 lectures in international or domestic conferences and seminers(41 lectures were invited lectures). In March 2010, I got Spring prize of Japanese mathematical society by"Study of representation theory of algebras and Cohen-Macaulay modules". On 2011 March, I got JSPS prize by"Representation theory of orders".

  • Research Products

    (73 results)

All 2012 2011 2010 2009 2006 Other

All Journal Article (21 results) (of which Peer Reviewed: 16 results) Presentation (51 results) Remarks (1 results)

  • [Journal Article] Preprojective algebras and c-sortable words2012

    • Author(s)
      Claire Amiot, Osamu Iyama Idun Reiten, Gordana Todorov
    • Journal Title

      Proc. Lond. Math. Soc

      Volume: 104 no.3 Pages: 513-539

    • Peer Reviewed
  • [Journal Article] Cluster tilting for higher Auslander algebras2011

    • Author(s)
      Osamu Iyama
    • Journal Title

      Adv. Math

      Volume: 226 Pages: 1-61

    • Peer Reviewed
  • [Journal Article] 2-Auslanderalgebras associated with reduced words in Coxeter groups2011

    • Author(s)
      Osamu Iyama, Idun Reiten
    • Journal Title

      Int. Math. Res. Not. IMRN

      Pages: 1782-1803

    • Peer Reviewed
  • [Journal Article] n-representation-finite algebras and twisted fractionally Calabi-Yau algebras2011

    • Author(s)
      Martin Herschend, Osamu Iyama
    • Journal Title

      Bull. Lond. Math. Soc

      Volume: 43 no.3 Pages: 449-466

    • Peer Reviewed
  • [Journal Article] Mutation of cluster-tilting objects and potentials2011

    • Author(s)
      Aslak Buan, Osamu Iyama, Idun Reiten, David Smith
    • Journal Title

      Amer. J. Math

      Volume: 133 no.4 Pages: 835-887

    • Peer Reviewed
  • [Journal Article] Stable categories of preprojective algebras and cluster categories2011

    • Author(s)
      Osamu Iyama
    • Journal Title

      Oberwolfach Report

      Pages: 600-603

  • [Journal Article] Steffen Oppermann, n-representation-finite algebras and n-APR tilting2011

    • Author(s)
      Osamu Iyama
    • Journal Title

      Trans. Amer. Math. Soc.

      Volume: 363 no.12 Pages: 6575-6614

    • Peer Reviewed
  • [Journal Article] Self injective quivers with potential and 2-representation-finite algebras2011

    • Author(s)
      Martin Herschend, Osamu Iyama
    • Journal Title

      Compos. Math

      Volume: 147 no.6 Pages: 1885-1920

    • Peer Reviewed
  • [Journal Article] Recollement of homotopy categories and Cohen-Macaulay modules2011

    • Author(s)
      Osamu Iyama Kiriko Kato, Jun-ichi Miyachi
    • Journal Title

      J. K-Theor

      Volume: 8 no.3 Pages: 507-542

    • Peer Reviewed
  • [Journal Article] Periodicities of T-systems and Y-systems2010

    • Author(s)
      Rei Inoue, Osamu Iyama, Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki
    • Journal Title

      Nagoya Math

      Volume: 197 Pages: 59-174

    • Peer Reviewed
  • [Journal Article] 整環の表現論-高次元Auslander-Reiten理論-2010

    • Author(s)
      Osamu Iyama
    • Journal Title

      2010年度日本数学会年会総合講演・企画特別講演アブストラクト

      Pages: 1-16

  • [Journal Article] The classification of special Cohen-Macaulay modules2010

    • Author(s)
      Osamu Iyama, Michael Wemyss
    • Journal Title

      Math. Z

      Volume: 265 Pages: 41-83

    • Peer Reviewed
  • [Journal Article] Stable categories of Cohen-Macaulay modules and cluster categories2010

    • Author(s)
      Osamu Iyama
    • Journal Title

      Oberwolfach Report

      Pages: 1338-1341

  • [Journal Article] Cluster structures for 2-Calabi-Yau categories and unipotent groups2009

    • Author(s)
      Aslak Buan, Osamu Iyama, Idun Reiten, Jeanne Scott
    • Journal Title

      Compos. Math

      Volume: 145 Pages: 1035-1079

    • Peer Reviewed
  • [Journal Article] 前射影多元環の傾理論2009

    • Author(s)
      Osamu Iyama
    • Journal Title

      2009年代数幾何学シンポジウム報告集

      Pages: 60-64

  • [Journal Article] Tilting and cluster tilting for quotient singularities2009

    • Author(s)
      Osamu Iyama, Ryo Takahashi
    • Journal Title

      第31回可換環論シンポジウム報告集

      Pages: 154-157

  • [Journal Article] Silting mutation in triangulated categories

    • Author(s)
      Takuma Aihara, Osamu Iyama
    • Journal Title

      J. Lond. Math. Soc.

      Volume: (to appear)(掲載確定)

    • Peer Reviewed
  • [Journal Article] A New Triangulated Category for Rational Surface Singularities

    • Author(s)
      Osamu Iyama, Michael Wemyss
    • Journal Title

      Illinois J. Math.

      Volume: (to appear)(掲載確定)

    • Peer Reviewed
  • [Journal Article] Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras I : Type B_r

    • Author(s)
      Rei Inoue, Osamu Iyama, Bernhard Keller, Atsuo Kuniba, Tomoki Nakanishi
    • Journal Title

      Publ. Res. Inst. Math. Sci.

      Volume: (to appear)(掲載確定)

    • Peer Reviewed
  • [Journal Article] Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras II : Type C_r, F_4, and G_2

    • Author(s)
      Rei Inoue, Osamu Iyama, Bernhard Keller, Atsuo Kuniba, Tomoki Nakanishi
    • Journal Title

      Publ. Res. Inst. Math. Sci.

      Volume: (to appear)(掲載確定)

    • Peer Reviewed
  • [Journal Article] On the Noncommutative Bondal-Orlov Conjecture

    • Author(s)
      Osamu Iyama, Michael Wemyss
    • Journal Title

      J. Reine Angew. Math.

      Volume: (to appear)(掲載確定)

    • Peer Reviewed
  • [Presentation] $¥tau$-tilting theory2012

    • Author(s)
      Osamu Iyama
    • Organizer
      Cluster categories and cluster tilting(招待講演)
    • Place of Presentation
      ノルウェー理工科大
    • Year and Date
      2012-03-28
  • [Presentation] Stable categories of Cohen-Macaulay modules and cluster categories2012

    • Author(s)
      Osamu Iyama
    • Organizer
      グラスゴー大学代数学セミナー(招待講演)
    • Place of Presentation
      グラスゴー大学
    • Year and Date
      2012-03-22
  • [Presentation] $n$-representation infinite algebras2012

    • Author(s)
      Osamu Iyama
    • Organizer
      エジンバラ大学代数学セミナー(招待講演)
    • Place of Presentation
      エジンバラ大学
    • Year and Date
      2012-03-20
  • [Presentation] Pseudo-tilting theory2012

    • Author(s)
      Osamu Iyama
    • Organizer
      Representation Theory of Chevalley Groups and Related Topics(招待講演)
    • Place of Presentation
      名古屋大学
    • Year and Date
      2012-03-15
  • [Presentation] Mutation in triangulated categories2012

    • Author(s)
      Osamu Iyama
    • Organizer
      第7回代数・解析・幾何学セミナー(招待講演)
    • Place of Presentation
      鹿児島大学
    • Year and Date
      2012-02-16
  • [Presentation] 準傾理論入門2012

    • Author(s)
      Osamu Iyama
    • Organizer
      第2回徳山環論セミナー(招待講演)
    • Place of Presentation
      徳山高専
    • Year and Date
      2012-01-08
  • [Presentation] Auslander correspondence and$ n$-representation finite algebras, Higher preprojective algebras and quives with potential2011

    • Author(s)
      Osamu Iyama
    • Organizer
      $n$-representation infinite algebras,第10回静岡代数学セミナー(招待講演)
    • Place of Presentation
      静岡大学
    • Year and Date
      20111202-04
  • [Presentation] Stable categories of Cohen-Macaulay modules and cluster categories(招待講演)2011

    • Author(s)
      Osamu Iyama
    • Organizer
      Derived Categories 2011 Tokyo
    • Place of Presentation
      東京大学
    • Year and Date
      20110124-28
  • [Presentation] ポテンシャル付き箙とAPR傾加群2011

    • Author(s)
      Osamu Iyama
    • Organizer
      信州代数セミナー(招待講演)
    • Place of Presentation
      信州大学
    • Year and Date
      2011-12-08
  • [Presentation] 安定圏,導来圏,団圏-環論の世界の拡がり-2011

    • Author(s)
      Osamu Iyama
    • Organizer
      信州代数談話会(招待講演)
    • Place of Presentation
      信州大学
    • Year and Date
      2011-12-07
  • [Presentation] $n$-representation infinite algebras2011

    • Author(s)
      Osamu Iyama
    • Organizer
      Shanghai Conference on Representation Theory of Algebras(招待講演)
    • Place of Presentation
      Shanghai Jiao Tong University
    • Year and Date
      2011-10-03
  • [Presentation] Tilting and cluster tilting for stable categories of Cohen-Macaulay modules2011

    • Author(s)
      Osamu Iyama
    • Organizer
      Noncom mutative Algebraic Geometry(招待講演)
    • Place of Presentation
      Fudan University
    • Year and Date
      2011-09-16
  • [Presentation] Auslander-Reiten duality and maximal modification algebras for non-isolated singularities2011

    • Author(s)
      Osamu Iyama
    • Organizer
      リンカーン大学代数学セミナー(招待講演)
    • Place of Presentation
      リンカーン大学
    • Year and Date
      2011-09-01
  • [Presentation] Calabi-Yau reduction for hypersurface singularities2011

    • Author(s)
      Osamu Iyama
    • Organizer
      カンザス大学代数学セミナー(招待講演)
    • Place of Presentation
      カンザス大学
    • Year and Date
      2011-08-30
  • [Presentation] Cluster algebras and categorification2011

    • Author(s)
      Osamu Iyama
    • Organizer
      Infinite Analysis 11(招待講演)
    • Place of Presentation
      名古屋大学
    • Year and Date
      2011-08-24
  • [Presentation] Auslander-Reiten duality for Cohen-Macaulay modules2011

    • Author(s)
      Osamu Iyama
    • Organizer
      第8回可換環論サマースクール
    • Place of Presentation
      名古屋大学
    • Year and Date
      2011-08-24
  • [Presentation] Tilting and cluster tilting for Cohen-Macaulay modules2011

    • Author(s)
      Osamu Iyama
    • Organizer
      第5回大和郡山セミナー(招待講演)
    • Place of Presentation
      奈良高専
    • Year and Date
      2011-05-22
  • [Presentation] Higher preprojective algebras and their stable categories2011

    • Author(s)
      Osamu Iyama
    • Organizer
      大阪市立大学代数学セミナー(招待講演)
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2011-05-17
  • [Presentation] Tilting and cluster tilting for stable categories of Cohen-Macaulay modules2011

    • Author(s)
      Osamu Iyama
    • Organizer
      大阪表現論セミナー(招待講演)
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2011-05-16
  • [Presentation] Tilting and cluster tilting for stable categories of Cohen-Macaulay modules2011

    • Author(s)
      Osamu Iyama
    • Organizer
      Workshop on Matrix Factorizations(招待講演)
    • Place of Presentation
      University of Bielefeld
    • Year and Date
      2011-05-07
  • [Presentation] Stable categories of Cohen-Macaulay modules and cluster categories2011

    • Author(s)
      Osamu Iyama
    • Organizer
      セミナー
    • Place of Presentation
      Norges Teknisk-Naturvitenskapelige Universitet
    • Year and Date
      2011-03-24
  • [Presentation] Algebraic McKay correspondence and cluster tilting2011

    • Author(s)
      Osamu Iyama
    • Organizer
      Workshop on non-commutative geometry and the McKay correspondence
    • Place of Presentation
      名古屋大学
    • Year and Date
      2011-03-15
  • [Presentation] Stable categories of Cohen-Macaulay modules and cluster categories2011

    • Author(s)
      Osamu Iyama
    • Organizer
      Representation Theory of Quivers and Finite Dimensional Algebras(招待講演)
    • Place of Presentation
      Mathematisches Forschungsinstitut Oberwolfach
    • Year and Date
      2011-02-22
  • [Presentation] Tilting theory and Cohen-Macaulay modules2011

    • Author(s)
      Osamu Iyama
    • Organizer
      第5回岡山大学環論セミナー
    • Place of Presentation
      岡山大学
    • Year and Date
      2011-02-14
  • [Presentation] Self injective quivers with potential and 2-representation-finite algebras2010

    • Author(s)
      Osamu Iyama
    • Organizer
      セミナー(招待講演)
    • Place of Presentation
      Universitaet Koeln
    • Year and Date
      20101810
  • [Presentation] Calabi-Yau triangulated categories and Cluster tilting2010

    • Author(s)
      Osamu Iyama
    • Organizer
      Derived categories, mirror symmetry and McKay correspondence Seminar(招待講演)
    • Place of Presentation
      華東師範大学
    • Year and Date
      20101129-30
  • [Presentation] 1. Representation theory of Cohen-Macaulay modules I : Classical theory, 2. Representation theory of Cohen-Macaulay modules II : Connection to cluster categories2010

    • Author(s)
      Osamu Iyama
    • Organizer
      連続講演(招待講演)
    • Place of Presentation
      清華大学
    • Year and Date
      20101003-09
  • [Presentation] 1. n-representation-finite algebras, 2. n-representation-infinite algebras and application to representation dimension, 3. Cluster tilting in 2-Calabi-Yau triangulated categories2010

    • Author(s)
      Osamu Iyama
    • Organizer
      連続講演(招待講演)
    • Place of Presentation
      南京大学
    • Year and Date
      20100925-30
  • [Presentation] Stable categories of Cohen-Macaulay modules, Advanced School and Conference on Homological and Geometrical Methods in Representation Theory2010

    • Author(s)
      Osamu Iyama
    • Organizer
      International Center for Theoretical Physics
    • Place of Presentation
      Trieste, Italy.
    • Year and Date
      20100118-0205
  • [Presentation] Stable categories of Cohen-Macaulay modules and cluster categories2010

    • Author(s)
      Osamu Iyama
    • Organizer
      Shanghai workshop on representation theory
    • Place of Presentation
      華東師範大学
    • Year and Date
      2010-12-11
  • [Presentation] Cotilting modules VS Canonical module2010

    • Author(s)
      Osamu Iyama
    • Organizer
      第3回大和郡山セミナー(招待講演)
    • Place of Presentation
      奈良高専
    • Year and Date
      2010-11-14
  • [Presentation] Quiver mutation and cluster tilting2010

    • Author(s)
      Osamu Iyama
    • Organizer
      談話会(招待講演)
    • Place of Presentation
      清華大学
    • Year and Date
      2010-10-08
  • [Presentation] Silting mutation in triangulated categories2010

    • Author(s)
      Osamu Iyama
    • Organizer
      談話会(招待講演)
    • Place of Presentation
      南京師範大学
    • Year and Date
      2010-09-27
  • [Presentation] Stable categories of Cohen-Macaulay modules and cluster categories(招待講演)2010

    • Author(s)
      Osamu Iyama
    • Organizer
      Test problems for the theory of finite dimensional algebras
    • Place of Presentation
      Banff International Research Station
    • Year and Date
      2010-09-16
  • [Presentation] Stable categories of Cohen-Macaulay modules and cluster categories2010

    • Author(s)
      Osamu Iyama
    • Organizer
      XIV International Conference on Representations of Algebras and Workshop
    • Place of Presentation
      National OlympicsMemorial Youth Center
    • Year and Date
      2010-08-10
  • [Presentation] Stable categories of Cohen-Macaulay modules and cluster categories2010

    • Author(s)
      Osamu Iyama
    • Organizer
      セミナー(招待講演)
    • Place of Presentation
      Universitaet Bonn
    • Year and Date
      2010-05-17
  • [Presentation] Selfinjective quivers with potential and 2-representation-finite algebras2010

    • Author(s)
      Osamu Iyama
    • Organizer
      Interactions between Algebraic Geometry and Noncom mutative Algebra(招待講演)
    • Place of Presentation
      Mathematisches Forschungsinstitut Oberwolfach
    • Year and Date
      2010-05-14
  • [Presentation] 2-Auslander algebras associated with reduced words in Coxetergroups2010

    • Author(s)
      Osamu Iyama
    • Organizer
      Interplay between representation theory and geometry(招待講演)
    • Place of Presentation
      清華大学
    • Year and Date
      2010-05-06
  • [Presentation] 整環の表現論-高次元Auslander-Reiten理論-2010

    • Author(s)
      Osamu Iyama
    • Organizer
      2010年度日本数学会年会,春季賞受賞講演(招待講演)
    • Place of Presentation
      Keio University, Japan
    • Year and Date
      2010-03-25
  • [Presentation] Cluster tilting fornon-isolated singularities2009

    • Author(s)
      Osamu Iyama
    • Organizer
      Kinosaki Symposium on Algebraic Geometry(招待講演)
    • Place of Presentation
      Kinosaki, Japan
    • Year and Date
      20091126-30
  • [Presentation] Tilting and cluster tilting for quotient singularities2009

    • Author(s)
      Osamu Iyama
    • Organizer
      The 31st Symposium on Commutative Algebra
    • Place of Presentation
      Hotel Awina-Osaka, Japan
    • Year and Date
      20091124-27
  • [Presentation] Cluster tilting for hypersurface singularities2009

    • Author(s)
      Osamu Iyama
    • Organizer
      Seminar on Cohen-Macaulay modules
    • Place of Presentation
      Osaka Prefecture University, Japan
    • Year and Date
      20091122-23
  • [Presentation] Cluster tilting2009

    • Author(s)
      Osamu Iyama
    • Organizer
      琉球大学セミナー
    • Place of Presentation
      琉球大学
    • Year and Date
      20091008-13
  • [Presentation] T-systems, cluster algebras and cluster categories IV2009

    • Author(s)
      Osamu Iyama
    • Organizer
      q-変形された対称関数とその周辺(招待講演)
    • Place of Presentation
      Japan
    • Year and Date
      20090909-12
  • [Presentation] Cluster tilting theory, Representation Theory and Combinatorics(招待講演)2009

    • Author(s)
      Osamu Iyama
    • Organizer
      Morningside Center of Mathematics
    • Place of Presentation
      Beijing, China
    • Year and Date
      20090831-04
  • [Presentation] Auslander algebras preprojective algebras and Calabi-Yaualgebras2009

    • Author(s)
      Osamu Iyama
    • Organizer
      Noncom mutative Algebraic Geometry and Related Topics(招待講演)
    • Place of Presentation
      Research Institute for Mathematical Sciences
    • Year and Date
      20090824-28
  • [Presentation] n-representation finite algebras, Homological and geometric methods in algebra(招待講演)2009

    • Author(s)
      Osamu Iyama
    • Organizer
      Norwegian University of Technology and Science
    • Place of Presentation
      Trondheim, Norway
    • Year and Date
      20090810-14
  • [Presentation] Cluster tilting in singularity theory I2009

    • Author(s)
      Osamu Iyama
    • Organizer
      Workshop on Triangulated Categories and Singularities(招待講演)
    • Place of Presentation
      Universitaet Paderborn, Germany
    • Year and Date
      20090525-30
  • [Presentation] Introduction to cluster tilting in 2-Calabi-Yau categories2009

    • Author(s)
      Osamu Iyama
    • Organizer
      12nd Symposium on Representation Theory of Algebraic groups and Quantum groups(招待講演)
    • Place of Presentation
      Katsuura, Japan
    • Year and Date
      20090510-15
  • [Presentation] 箙の変異と団傾理論(招待講演)2006

    • Author(s)
      Osamu Iyama
    • Organizer
      談話会
    • Place of Presentation
      筑波大学
    • Year and Date
      20062410
  • [Presentation] Triangulated categories in representation theory of associative algebras(招待講演)2006

    • Author(s)
      Osamu Iyama
    • Organizer
      Lefschetz fibration and category theory
    • Place of Presentation
      大阪大学
    • Year and Date
      2006-05-10
  • [Remarks]

    • URL

      http://www.math.nagoya-u.ac.jp/~iyama

URL: 

Published: 2013-07-31  

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