Representation theory of Orders

• Project/Area Number: 18740007
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Nagoya University
• Principal Investigator: IYAMA Osamu Nagoya University, 大学院・多元数理科学研究科, 准教授 (70347532)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,730,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2007: ¥1,100,000 (Direct Cost: ¥1,100,000); Fiscal Year 2006: ¥1,200,000 (Direct Cost: ¥1,200,000)
• Keywords: 高次元Auslander-Reiten理論 / n-クラスター傾部分圏 / 高次元Auslander多元環 / 変異 / Cohen-Macaulay加群 / Calabi-Yau三角圏 / preprojective多元環 / クラスター多元環 / Auslander-Reiten理論 / Auslander多元環 / $n$-クラスター傾対象 / $n$-有限表現型 / $n$-クラスター傾部分圏 / Calabi-Yau多元環 / $n$-完備多元環 / n-クラスター傾斜部分圏 / mutation / Calabi-Yau的三角圏 / 1次元超曲面特異点 / 非可換クレパント解消

Research Abstract

高次元Auslander-Reiten理論としてn-クラスター傾部分圏を調べた。2007年の第12回多元環の表現論国際集会のワークショップでは3回の全体講演を行い、第一回ICRA Awardを受賞した。受賞題目は「Higher theory for almost split sequences and Auslander correspondence, and subsequent work on Calabi-Yau categories」。2008年度数学会年会では代数学賞を受賞した。受賞題目は「高次Auslander-Reiten理論の研究」。

Research Products

• [Journal Article] Fomin-Zelevinsky mutation and tilting modules over Calabi-Yau algebras (2008)
  • Author(s): Osamu Iyama, Idun Reiten
  • Journal Title: Amer. J. Math. 130 no. 4 Pages: 1087-1149
  • Peer Reviewed
• [Journal Article] Cluster tilting in 2-Calabi-Yau categories II (2008)
  • Author(s): Osamu Iyama
  • Journal Title: Oberwolfach Report Pages: 410-414
• [Journal Article] Cluster tilting for one-dimensional hypersurface singularities (2008)
  • Author(s): Igor Burban, Osamu Iyama, Bernhard Keller, Idun Reiten
  • Journal Title: Adv. Math. 217 no. 6 Pages: 2443-2484
  • Peer Reviewed
• [Journal Article] Mutation in triangulated categories and rigid Cohen-Macaulay modules (2008)
  • Author(s): Osamu Iyama, Yuji Yoshino
  • Journal Title: Invent. Math. 172 no. 1 Pages: 117-168
  • Peer Reviewed
• [Journal Article] Fomin-Zelevinsky mutation and tilting modules over Calabi-Yau algebras (2008)
  • Author(s): Osamu Iyama, Idun Reiten
  • Journal Title: American Journal of Mathematics 103 Pages: 1087-1149
  • Peer Reviewed
• [Journal Article] Auslander-Reiten theory revisited (2008)
  • Author(s): Osamu Iyama
  • Journal Title: Trends in Representation Theory of Algebras and Related Topics, European Mathematical Society Pages: 349-398
  • Peer Reviewed
• [Journal Article] Cluster tilting in 2-Calabi-Yau categories II (2008)
  • Author(s): Osamu Iyama
  • Journal Title: Oberwolfach Report 9 Pages: 410-7414
  • Peer Reviewed
• [Journal Article] Mutation in triangulated categories and rigid Cohen-Macaulay modules (2008)
  • Author(s): Osamu lyama, Yiji Yoshino
  • Journal Title: Inventiones Mathematicae 172 Pages: 117-168
  • Peer Reviewed
• [Journal Article] Cluster tilting for one-dimensional hypersurface singularities (2008)
  • Author(s): lgor Burban, Osamu lyama, Bernhard Keller, ldun Reiten
  • Journal Title: Advances in Mathematics 217 Pages: 2443-2484
  • Peer Reviewed
• [Journal Article] Auslander-type conditions and cotorsion pairs (2007)
  • Author(s): Zhaoyong Huang, Osamu Iyama
  • Journal Title: J. Algebra 318 no. 1 Pages: 93-110
  • Peer Reviewed
• [Journal Article] Auslander correspondence (2007)
  • Author(s): Osamu Iyama
  • Journal Title: Adv. Math. 210 no. 1 Pages: 51-82
  • Peer Reviewed
• [Journal Article] Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories (2007)
  • Author(s): Osamu Iyama
  • Journal Title: Adv. Math. 210 no. 1 Pages: 22-50
  • Peer Reviewed
• [Journal Article] Auslander-type conditions and cotorsion pairs (2007)
  • Author(s): Osamu lyama, Zhaoyong Huang
  • Journal Title: Journal of Algebra 318 Pages: 93-110
  • Peer Reviewed
• [Journal Article] Higher dimensional Auslander Reiter theory on maximal orthogonal subcategories (2007)
  • Author(s): O.Iyama
  • Journal Title: Advances in Mathematics 210-1 Pages: 22-50
• [Journal Article] Auslander correspondence (2007)
  • Author(s): O.Iyama
  • Journal Title: Advances in Mathmatics 210-1 Pages: 51-82
• [Journal Article] Tilting modules over Calabi-Yau algebras (2006)
  • Author(s): Osamu Iyama
  • Journal Title: Oberwolfach Report Pages: 492-494
• [Journal Article] Auslander-Reiten theory revisited, Trends in Representation Theory of Algebras and Related Topics
  • Author(s): Osamu Iyama
  • Journal Title: European Mathematical Society 2008 Pages: 349-398
  • Peer Reviewed
• [Journal Article] Cluster structures for 2-Calabi-Yau categories and unipotent groups
  • Author(s): Aslak Buan, Osamu Iyama, Idun Reiten, Jeanne Scott
  • Journal Title: Compos. Math. (掲載決定済み)
  • Peer Reviewed
• [Journal Article] Michael Wemyss, The Classification of Special Cohen-Macaulay Modules
  • Author(s): Osamu Iyama
  • Journal Title: Math. Z. (掲載決定済み)
  • Peer Reviewed
• [Journal Article] Fomin-Zelevinsky mutation and tilting modules over Calabi-Yau algebras
  • Author(s): O.Iyama, I.Reiten
  • Journal Title: American Journal of Mathematics (掲載予定)
• [Presentation] n-representation-finite algebras of type A (2009)
  • Author(s): Osamu Iyama
  • Organizer: Workshop on Representations and Cohomology
  • Place of Presentation: University of Cologne, Germany
• [Presentation] n-representation-finite algebras of type A (2009)
  • Author(s): Osamu Iyama
  • Organizer: Workshop on Representations and Cohomology
  • Place of Presentation: Cologne, Germany
• [Presentation] (i) Mini-course - Introduction to the Auslander-Reiten theory, (ii) n-cluster tilting and n-APR tilting (2008)
  • Author(s): Osamu Iyama
  • Organizer: 63rd Algebra Day
  • Place of Presentation: Carleton University, Ottawa, Canada
  • Year and Date: 2008-09-13
• [Presentation] (1) Mini-course-Introduction to the Auslander-Reiten theory (2) n-cluster tilting and n-APR tilting (2008)
  • Author(s): Osamu Iyama
  • Organizer: 63 rd Algebra Day
  • Place of Presentation: Ottawa, Canada
  • Year and Date: 2008-09-13
• [Presentation] Auslander-Reiten理論の高次元化に向けて (2008)
  • Author(s): Osamu Iyama
  • Organizer: Lecture for Algebra Prize of the Mathematical Society of Japan
  • Place of Presentation: Osaka
  • Year and Date: 2008-03-25
• [Presentation] Auslander-Reiten理論の高次元化に向けて(代数学賞受賞特別講演) (2008)
  • Author(s): Osamu lyama
  • Organizer: 2008年度日本数学会年会
  • Place of Presentation: Osaka, Japan
  • Year and Date: 2008-03-25
• [Presentation] Cluster tilting for one-dimensional hypersurface singularities (2008)
  • Author(s): Osamu lyama
  • Organizer: Intemational Conference on Commutative Algebra
  • Place of Presentation: Yokohama, Japan
  • Year and Date: 2008-03-19
• [Presentation] Cluster tilting in 2-Calabi-Yau categories (2008)
  • Author(s): Osamu lyama
  • Organizer: Representation Theory of Finite Dimensional Alqebras
  • Place of Presentation: Oberwolfach, Germany
  • Year and Date: 2008-02-18
• [Presentation] 2-Calabi-Yau categories associated with Coxeter group elements (2008)
  • Author(s): Osamu Iyama
  • Organizer: International Conference and Workshop on Cluster Algebras and Related Topics
  • Place of Presentation: Mexico
• [Presentation] Tiling and cluster tilting for quotient singularities (2008)
  • Author(s): Osamu Iyama
  • Organizer: Representation theory of finite groups and algebras, and related topics
  • Place of Presentation: Research Institute for Mathematical Sciences, Kyoto, Japan.
• [Presentation] Cluster tilting in 2-Calabi-Yau categories (2008)
  • Author(s): Osamu Iyama
  • Organizer: Interactions Between Noncommutative Algebra and Algebraic Geometry
  • Place of Presentation: Banff International Research Station, Canada
• [Presentation] n-cluster tilting and n-APR tilting (2008)
  • Author(s): Osamu Iyama
  • Organizer: XXth Meeting on Representation Theory of Algebras
  • Place of Presentation: Universite de Sherbrooke, Sherbrooke, Canada
• [Presentation] Introduction to cluster tilting in 2-Calabi-Yau categories (2008)
  • Author(s): Osamu Iyama
  • Organizer: Expansion of Combinatorial Representation Theory
  • Place of Presentation: Research Institute for Mathematical Sciences, Kyoto, Japan
• [Presentation] Cluster tilting for one-dimensional hypersurface singularities (2008)
  • Author(s): Osamu Iyama
  • Organizer: Interactions between Representation Theory and Commutative Algebra
  • Place of Presentation: Barcelona, Spain
• [Presentation] Tiling and cluster tilting objects for quotient singularities (2008)
  • Author(s): Osamu Iyama
  • Organizer: Spectral Methods in Representation Theory of Algebras and Applications to the Study of Rings of Singularities
  • Place of Presentation: Banff International Research Station, Canada
• [Presentation] Tilting mutation and its application (2008)
  • Author(s): Osamu Iyama
  • Organizer: 41st Ring and Representation theory symposium
  • Place of Presentation: Shizuoka, Japan
• [Presentation] Cluster tilting in 2-Calabi-Yau categories (2008)
  • Author(s): Osamu Iyama
  • Organizer: Workshop "Crystals and Tropical Combinatorics"
  • Place of Presentation: Kyoto, Japan
• [Presentation] n-cluster tilting for higher Auslander algebras (2008)
  • Author(s): Osamu Iyama
  • Organizer: XIII International Conference on Representations of Algebras
  • Place of Presentation: Sao Paulo, Brazil
• [Presentation] n-cluster tilting and n-APR tilting (2008)
  • Author(s): Osamu Iyama
  • Organizer: Mini-Symposium on ring theory in connection with representation theory and homological algebra
  • Place of Presentation: Osaka, Japan
• [Presentation] Recollement of homotopy categories and Cohen-Macaulay modules (2008)
  • Author(s): Osamu Iyama
  • Organizer: Representation Theory of Algebras
  • Place of Presentation: Tehran, Iran
• [Presentation] (i) The finiteness of the representation dimension, (ii) Construction of algebras of finite global dimension as endomorphism algebras of n-cluster tilting objects (2008)
  • Author(s): Osamu Iyama
  • Organizer: The Representation Dimension of Artin Algebras
  • Place of Presentation: University of Bielefeld, Germany
• [Presentation] Mutation of cluster tilting object and potentials (2008)
  • Author(s): Osamu Iyama
  • Organizer: Maurice Auslander Distinguished Lectures and International Conference
  • Place of Presentation: Massachusetts, USA
• [Presentation] Cluster tilting for one-dimensional hypersurface singularities (2008)
  • Author(s): Osamu Iyama
  • Organizer: International Conference on Commutative Algebra
  • Place of Presentation: Yokohama, Japan
• [Presentation] Cluster tilting in 2-Calabi-Yau categories II (2008)
  • Author(s): Osamu Iyama
  • Organizer: Representation Theory of Finite Dimensional Algebras
  • Place of Presentation: Mathematisches Forschungsinstitut Oberwolfach, Germany
• [Presentation] (1) The finiteness of the representation dimension (2) Construction of algebras of finite global dimension as endomorphism algebras of n-cluster tilting objects (2008)
  • Author(s): Osamu Iyama
  • Organizer: The Representation Dimention of Artin Algebras
  • Place of Presentation: Bielefeld, Germany
• [Presentation] Tilting mutation and its application (2008)
  • Author(s): Osamu Iyama
  • Organizer: 41st Ring and Representation theory symposiuni
  • Place of Presentation: Shizuoka, Japan
• [Presentation] Tilting and cluster tilting objects for quotient singularities (2008)
  • Author(s): Osamu Iyama
  • Organizer: Spectral Methods in Representation Theory of Algebras and Applications to the Study of Rings of Singularities
  • Place of Presentation: Banff, Canada
• [Presentation] Cluster tilting for one-dimensional hypersurface singularities (2008)
  • Author(s): Osamu Iyama
  • Organizer: Interactions between Representation Theory and Commutative Algebra
  • Place of Presentation: Bercelona, Spain
• [Presentation] Introduction to cluster tilting in 2-Calabi-Yau categories (2008)
  • Author(s): Osamu Iyama
  • Organizer: Expansion of Combinatorial Representation Theory
  • Place of Presentation: Kyoto, Japan
• [Presentation] n-cluster tilting and n-APR tilting (2008)
  • Author(s): Osamu Iyama
  • Organizer: XXth Meeting on Representation Theory of Algebras
  • Place of Presentation: Sherbrooke, Canada
• [Presentation] Cluster tilting in 2-Calabi-Yau categories (2008)
  • Author(s): Osamu Iyama
  • Organizer: Interactions Between Noncommutative Algebra and Algebraic Geometry
  • Place of Presentation: Banff, Canada
• [Presentation] Tilting and cluster tilting for quotient singularities (2008)
  • Author(s): Osamu Iyama
  • Organizer: Representation theory of finite groups and algebras, and related topics
  • Place of Presentation: Kyoto, Japan
• [Presentation] 2-Calabi-Yau categories associated with Coxeter group elements (2008)
  • Author(s): Osamu Iyama
  • Organizer: International Conference and Workshop on Cluster Algebras and Related Topics
  • Place of Presentation: Mexice city, Mexico
• [Presentation] Cluster tilting for one-dimensional hypersurtace singularities (2007)
  • Author(s): Osamu lyama
  • Organizer: Categorical Aspects of Algebraic Geometry in Mirror Symmetry
  • Place of Presentation: Kyoto, Japan
  • Year and Date: 2007-12-06
• [Presentation] Tilting modules over Calabi-Yau algebras (2007)
  • Author(s): Osamu lyama
  • Organizer: Calabi-Yau algebras and N-Koszul algebras
  • Place of Presentation: Luminy, France
  • Year and Date: 2007-10-25
• [Presentation] Construction of algebras with $n$-cluster tilting objects (2007)
  • Author(s): Osamu lyama
  • Organizer: Workshop on Categorification, Quantization and Clusters
  • Place of Presentation: Beijing, China
  • Year and Date: 2007-09-13
• [Presentation] Auslander algebras of dimension three (2007)
  • Author(s): Osamu lyama
  • Organizer: Perspectives in Auslander-Reiten Theory
  • Place of Presentation: Trondheim, Norway
  • Year and Date: 2007-05-10
• [Presentation] Cluster tilting for one-dimensional hypersurface singularities (2007)
  • Author(s): Osamu Iyama
  • Organizer: Categorical Aspects of Algebraic Geometry in Mirror Symmetry
  • Place of Presentation: Research Institute for Mathematical Sciences, Japan
• [Presentation] Tilting modules over Calabi-Yau algebras (2007)
  • Author(s): Osamu Iyama
  • Organizer: Calabi-Yau algebras and N-Koszul algebras
  • Place of Presentation: CIRM, France
• [Presentation] Construction of algebras with n-cluster tilting objects (2007)
  • Author(s): Osamu Iyama
  • Organizer: Workshop on Categorification, Quantization and Clusters
  • Place of Presentation: Morningside Center of Mathematics, Beijing, China
• [Presentation] Auslander-Reiten theory revisited (2007)
  • Author(s): Osamu Iyama
  • Organizer: XII International Conference on Representations of Algebras
  • Place of Presentation: Torun, Poland
• [Presentation] Auslander algebras of dimension three (2007)
  • Author(s): Osamu Iyama
  • Place of Presentation: Norwegian University of Technology and Science, Trondheim, Norway
• [Presentation] Mutations in triangulated categories and rigid Cohen-Macaulay modules (2006)
  • Author(s): Osamu Iyama
  • Organizer: Workshop on Triangulated Categories
  • Place of Presentation: University of Leeds, England
• [Presentation] Mutation and tilting modules, (2006)
  • Author(s): Osamu Iyama
  • Organizer: Cluster Algebras and Cluster Tilted Algebra
  • Place of Presentation: University of Bielefeld, Germany
• [Remarks] ホームページ等
  • URL: http://www.math.nagoya-u.ac.jp/~iyama/