Applications of representation theory and commutative ring theory to classification problems in noncommutative algebraic geometry

• Project/Area Number: 19540020
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Shizuoka University
• Principal Investigator: MORI IZURU Shizuoka University, 理学部, 准教授 (50436903)
• Project Period (FY): 2007 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 環論 / 非可換代数幾何学 / 多元環の表現論 / 可換環論 / AS-regular algebra / 量子線織曲面 / Ext群 / 三角圏

Research Abstract

非可換代数幾何学において量子射影空間や量子線織曲面は主要な研究対象である。この研究課題では大きく分けて次の三つの成果を得た。(1)可換環論を用いて非可換代数多様体上に交叉理論を展開し、量子線織曲面の幾何を解明した。(2)有限次元多元環の表現論を用いて、量子射影空間の座標環であるAS-regular algebraの構造を決定した。(3)量子射影空間の分類と大局次元有限の有限次元多元環の分類の間に密接な関係があることを示した。

Research Products

• [Journal Article] Quantum ruled surfaces defined by quivers (2009)
  • Author(s): Izuru Mori
  • Journal Title: 2009代数幾何学シンポジウム記録 Pages: 65-75
  • NAID: 120005763714
• [Journal Article] Asymmetry of Ext-groups (2009)
  • Author(s): Izuru Mori
  • Journal Title: J. Algebra 322 Pages: 2235-2250
  • NAID: 120001788215
  • Peer Reviewed
• [Journal Article] On the classification of decomposable quantum ruled surfaces, Ring Theory 2007 (2009)
  • Author(s): Izuru Mori
  • Journal Title: World Sci. Publ Pages: 126-140
  • Peer Reviewed
• [Journal Article] On the classification of decomposable quantum ruled surfaces (2009)
  • Author(s): Izuru Mori
  • Journal Title: Ring Theory 2007 World Sclentific Pages: 126-140
  • Peer Reviewed
• [Journal Article] Co-point modules over Frobenius Koszul algebras (2008)
  • Author(s): Izuru Mori
  • Journal Title: Comm. Algebra 36 Pages: 4659-4677
  • Peer Reviewed
• [Journal Article] An introduction to noncommutative algebraic geometry (2008)
  • Author(s): Izuru Mori
  • Journal Title: Proceedings of the 40th Symposium on Ring Theory and Representation Theory Pages: 53-59
• [Journal Article] An introduct ion to noncommutative algebraic geometry (2008)
  • Author(s): Izuru Mori
  • Journal Title: Proceedings of the 40^<th> Symposium on Ring Theory and Representation Theory Pages: 53-59
• [Journal Article] Symmetry in the vanishing of Ext-groups (2007)
  • Author(s): Izuru Mori
  • Journal Title: Proceedings of the 39th Symposium on Ring Theory and Representation Theory Pages: 79-86
• [Journal Article] Intersection theory over quantum ruled surfaces (2007)
  • Author(s): Izuru Mori
  • Journal Title: J. Pure Appl. Algebra 221 Pages: 25-41
  • Peer Reviewed
• [Journal Article] Symmetry in the vanishing of Ext over stably symmetric algebras (2007)
  • Author(s): Izuru Mori
  • Journal Title: J. Algebra 310 Pages: 708-729
  • Peer Reviewed
• [Journal Article] Svmmetxy in the vanishing of Ext over stably symmetric algebras (2007)
  • Author(s): Izuru Mori
  • Journal Title: J.Algebia 310 Pages: 708-729
  • Peer Reviewed
• [Journal Article] Intersection theory over quantum ruled surfaces (2007)
  • Author(s): Izuru Mori
  • Journal Title: J.PureAppl.Algebra 211 Pages: 25-41
  • Peer Reviewed
• [Journal Article] Symmetiy in the vanishing of Ext-groups (2007)
  • Author(s): Iziuu Mori
  • Journal Title: Proceedings of the 39th Symposium on Ring Theory and Representation Theory Pages: 79-86
• [Presentation] Classification problems in noncommutative algebraic geometry and representation theory (2010)
  • Author(s): Izuru Mori
  • Organizer: 日本数学会年会
  • Place of Presentation: 慶應義塾大学
  • Year and Date: 2010-03-25
• [Presentation] Classification problems in noncommutative algebraic geometry and representation theory (2010)
  • Author(s): 毛利出
  • Organizer: 日本数学会年会代数学分科会特別講演
  • Place of Presentation: 慶應義塾大学
  • Year and Date: 2010-03-25
• [Presentation] Trivial extensions, preprojective algebras and AS-Gorenstein algebras, Special session on noncommutative ring theory (2009)
  • Author(s): Izuru Mori
  • Organizer: Joint Meeting of the KMS and AMS
  • Place of Presentation: Seoul, Korea
  • Year and Date: 2009-12-17
• [Presentation] Quantum ruled surfaces defined by quivers (2009)
  • Author(s): Izuru Mori
  • Organizer: 代数幾何学城崎シンポジウム
  • Place of Presentation: 城崎、兵庫
  • Year and Date: 2009-10-29
• [Presentation] B-construction and C-construction, Special session on quantum algebras and related topics (2008)
  • Author(s): Izuru Mori
  • Organizer: Joint Meeting of the AMS and SMS
  • Place of Presentation: Shanghai, China
  • Year and Date: 2008-12-18
• [Presentation] Noncommutative projective schemes associated to preprojective algebras and Koszul duality (2008)
  • Author(s): Izuru Mori
  • Organizer: Interactions between noncommutative algebra and algebraic geometry
  • Place of Presentation: Banff International Research Station, Banff, AB, Canada
  • Year and Date: 2008-10-31
• [Presentation] Homological properties of connected graded algebras (2008)
  • Author(s): Izuru Mori
  • Organizer: 空間の代数的・幾何的モデルとその周辺2008
  • Place of Presentation: 信州大学、長野
  • Year and Date: 2008-09-12
• [Presentation] Symmetry and asymmetry of the Euler form (2008)
  • Author(s): Izuru Mori
  • Organizer: Commutative algebra: Connections with algebraic topology and representation theory
  • Place of Presentation: University of Nebraska, Lincoln, U.S. A
  • Year and Date: 2008-05-20
• [Presentation] Symmetry and asymmetry of the Euler form (2008)
  • Author(s): Izuru Mori
  • Organizer: Commutative Algebra : Connections with Alge braic Topology and Representation Theory
  • Place of Presentation: University of Nebraska Lincoln
  • Year and Date: 2008-05-20
• [Presentation] An introduction to noncommutative algebraic geometry (2007)
  • Author(s): Izuru Mori
  • Organizer: 第5回日中韓環論国際シンポジウム
  • Place of Presentation: 国際オリンピック記念青少年センター
  • Year and Date: 2007-09-12
• [Presentation] Quantum ruled surfaces (2007)
  • Author(s): Izuru Mori
  • Organizer: 第52回代数学シンポジウム
  • Place of Presentation: 神戸大学、兵庫
  • Year and Date: 2007-08-09
• [Presentation] Quantum Ruled Surfaces (2007)
  • Author(s): 毛利 出
  • Organizer: 第52回代数学シンポジウム
  • Place of Presentation: 神戸大学百年記念館
  • Year and Date: 2007-08-09
• [Presentation] 非可換代数幾何学入門I・II (2007)
  • Author(s): Izuru Mori
  • Organizer: 玉原代数幾何セミナー2007
  • Place of Presentation: 東京大学玉原国際セミナーハウス、群馬
• [Remarks]
  • URL: http://www.ipc.shizuoka.ac.jp/~simouri/
• [Remarks]
  • URL: http://www.ipc.shizuoka.ac.jp/~simouri/
• [Remarks]
  • URL: http://www.ipc.shizuoka.ac.jp/~simouri/
• [Remarks]
  • URL: http://www.ipc.shizuoka.ac.Jp/~simouri/