Interactive developments of classification problems in noncommutative algebraic geometry and representation theory via triangulated categories

• Project/Area Number: 22540044
• 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 静岡大学, 理学部, 准教授 (50436903)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 環論 / 非可換代数幾何学 / 多元環の表現論 / AS-regular algebra / Fano algebra / McKay correspondence / AS-regular algebras / Fano algebras

Research Abstract

The major achievements of this research project are that we showed that there exist intimate relationships via triangulated categories between quantum projective spaces, which are important research objects in noncommutative algebraic geometry, and Fano algebras, which are important research objects in representation theory of finite dimensional algebras, and that we produced new results mainly in classification problems by applying results of noncommutative algebraic geometry and of representation theory of algebras to each other.

Research Products

• [Journal Article] Graded Morita equivalences for Geometric AS-regular algebras (2013)
  • Author(s): Izuru Moriand Kenta Ueyama
  • Journal Title: Glasg. Math. J Volume: 55 Pages: 241-257
  • Peer Reviewed
• [Journal Article] Graded Morita equivalences for geometric AS-regular algebras (2013)
  • Author(s): Izuru Mori and Kenta Ueyama
  • Journal Title: Glasgow Mathematical Journal Volume: 55 Issue: 2 Pages: 241-257
  • DOI: 10.1017/s001708951200047x
  • Peer Reviewed
• [Journal Article] Some derived equivalences between noncommutative schemes and algebras,DerivedCategoriesinAlgebraicGeometryTokyo2011 (2012)
  • Author(s): Izuru Mori
  • Journal Title: EMS Ser. Congr. Rep. Eur. Math. Soc., Zurich (2012 Pages: 185-196
  • Peer Reviewed
• [Journal Article] Some derived equivalences between noncommutative schemes and algebras (2012)
  • Author(s): Izuru Mori
  • Journal Title: EMS Ser. Congr. Rep., Eur. Math. Soc. Zurich Volume: ― Pages: 186-196
  • Peer Reviewed
• [Journal Article] Classification problems in noncommutative algebraic geometry and representation theory, Representations of Algebras and Related Topics (2011)
  • Author(s): Izuru Mori
  • Journal Title: EMS Ser. Congr. Rep. Eur. Math. Soc., Zurich (2011) Pages: 355-406
  • Peer Reviewed
• [Journal Article] The structure of AS-Gorenstein algebras (2011)
  • Author(s): Izuru Moriand Hiroyuki Minamoto
  • Journal Title: Adv. Math Volume: 226 Pages: 4061-4095
  • NAID: 120003291507
  • Peer Reviewed
• [Journal Article] Classification problems in noncommutative algebraic geometry and representation theory (2011)
  • Author(s): Izuru Mori
  • Journal Title: Representations of algebras and related topics Pages: 355-406
  • Peer Reviewed
• [Journal Article] The Structure of AS-Gorenstein Algebras (2011)
  • Author(s): Hiroyuki Minamoto, Izuru Mori
  • Journal Title: Advances in Mathematics Volume: 226 Pages: 4061-4095
  • NAID: 120003291507
  • Peer Reviewed
• [Journal Article] 「論説」非可換代数幾何学 「数学」 (2010)
  • Author(s): Izuru Mori
  • Journal Title: 日本数学会編集 岩波書店 Volume: 第62巻 第2号 Pages: 219-239
  • Peer Reviewed
• [Journal Article] 「論説」非可換代数幾何学 (2010)
  • Author(s): 毛利出
  • Journal Title: 「数学」日本数学会編集 岩波書店 Volume: 第62巻 Pages: 219-239
  • Peer Reviewed
• [Presentation] Points of a quantum plane (2013)
  • Author(s): Izuru Mori
  • Organizer: 第8回代数・解析・幾何学セミナー
  • Place of Presentation: 鹿児島大学 (招待講演)
  • Year and Date: 2013-02-19
• [Presentation] Points of a quantum plane (2013)
  • Author(s): Izuru Mori
  • Organizer: 第８回代数・解析・幾何学セミナー
  • Place of Presentation: 鹿児島大学 （鹿児島県）
  • Invited
• [Presentation] McKay type correspondence for AS-regular algebras (2012)
  • Author(s): Izuru Mori
  • Organizer: XV International conference on representations of algebras
  • Place of Presentation: Bielefeld University, Bielefeld, Germany
  • Year and Date: 2012-08-14
• [Presentation] Fixed subalgebras, skew group algebras and endomorphism algebras of AS-regular algebras (2012)
  • Author(s): Izuru Mori
  • Organizer: Linking representation theory, singularity theory and non-commutative algebraic geometry
  • Place of Presentation: Banff International Research Station, Banff, Canada (招待講演)
  • Year and Date: 2012-05-10
• [Presentation] McKay type correspondence for AS-regular algebras (2012)
  • Author(s): Izuru Mori
  • Organizer: Special session on noncommutative algebra and geometry
  • Place of Presentation: AMS Sectional Meeting, University of Hawaii, Honolulu, U.S.A
  • Year and Date: 2012-03-03
• [Presentation] McKay type correspondence for AS-regular algebras (2012)
  • Author(s): Izuru Mori
  • Organizer: American Mathematical Society Sectional Meeting
  • Place of Presentation: Honolulu, USA(招待講演)
  • Year and Date: 2012-03-03
• [Presentation] McKay type correspondence for AS-regular algebras (2012)
  • Author(s): Izuru Mori
  • Organizer: XV International Conference on Representations of Algebras
  • Place of Presentation: Bielefeld University (Germany)
• [Presentation] Fixed subalgebras, skew group algebras and endomorphism algebras of AS-regular algebras (2012)
  • Author(s): Izuru Mori
  • Organizer: Linking Representation Theory, Singularity Theory and Non-commutative Algebraic Geometry
  • Place of Presentation: Banff International Research Station (Canada)
  • Invited
• [Presentation] The structure of AS-regular algebras (2011)
  • Author(s): Izuru Mori
  • Organizer: Noncommutative algebraic geometry Shanghai workshop 2011
  • Place of Presentation: Fudan University, Shanghai, China (招待講演)
  • Year and Date: 2011-09-12
• [Presentation] The structure of AS-regular algebras (2011)
  • Author(s): Izuru Mori
  • Organizer: Noncommutative Algebraic Geometry Shanghai Workshop 2011
  • Place of Presentation: Shanghai, China(招待講演)
  • Year and Date: 2011-09-12
• [Presentation] Artin-Schelter Gorenstein algebras (2011)
  • Author(s): Izuru Mori
  • Organizer: RIMS 研究集会「空間の代数的・幾何的モデルとその周辺」
  • Place of Presentation: 京都大学数理解析研究所 (招待講演)
  • Year and Date: 2011-09-07
• [Presentation] McKay type correspondence for AS-regular algebras (2011)
  • Author(s): Izuru Mori
  • Organizer: 第6回日中韓環論国際シンポジウム
  • Place of Presentation: KyungHee University, Suwon, Korea (全体講演)
  • Year and Date: 2011-06-29
• [Presentation] McKay type correspondence for AS-regular algebras (Plenary talk) (2011)
  • Author(s): Izuru Mori
  • Organizer: The 6^<th> China-Japan-Korea International Conference on Ring Theory
  • Place of Presentation: Suwon, Korea(招待講演)
  • Year and Date: 2011-06-29
• [Presentation] McKay correspondence in noncommutative algebraic geometry (2011)
  • Author(s): Izuru Mori
  • Organizer: Workshop on Non-commutative geometry and the McKay correspondence
  • Place of Presentation: 名古屋大学 (招待講演)
  • Year and Date: 2011-03-15
• [Presentation] Fano algebras and quantum projective spaces (2011)
  • Author(s): Izuru Mori
  • Organizer: GCOE Conference "Derived categories 2011 Tokyo"
  • Place of Presentation: 東京大学 (招待講演)
  • Year and Date: 2011-01-26
• [Presentation] Quantum Beilinson algebras (2010)
  • Author(s): Izuru Mori
  • Organizer: Test problems for the theory of finite dimensional algebras
  • Place of Presentation: Banff International Research Station, Banff, Canada (招待講演)
  • Year and Date: 2010-09-16
• [Presentation] Classification problems in noncommutative algebraic geometry and representation theory (2010)
  • Author(s): Izuru Mori
  • Organizer: XIV International conference on representations of algebras
  • Place of Presentation: 国際オリンピック記念青少年センター, 東京 (全体講演)
  • Year and Date: 2010-08-12
• [Presentation] Classification Problems in Noncommutative Algebraic Geometry and Representation Theory (2010)
  • Author(s): Izuru Mori
  • Organizer: XIV International Conference on Representations of Algebras
  • Place of Presentation: 国際オリンピック記念青少年センター(東京都)
  • Year and Date: 2010-08-12
• [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/