Derived equivalences and Gorenstein dimension

• Project/Area Number: 26887034
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Tokyo Denki University
• Principal Investigator: KOGA Hirotaka 東京電機大学, 情報環境学部, 助教 (30736723)
• Project Period (FY): 2014-08-29 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000); Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 多元環の表現論 / 導来同値 / ゴレンシュタイン次元 / アーベル圏 / 代数学

Outline of Final Research Achievements

We introduce the notion of complexes of finite Gorenstein projective dimension and show that a derived equivalence induces an equivalence between the full triangulated subcategories consisting of complexes of finite Gorenstein projective dimension
provided that the equivalence satisfies a certain condition.

Research Products

• [Journal Article] Clifford extension (2015)
  • Author(s): M. Hoshino, N. Kameyama and H. Koga
  • Journal Title: Comm. Algebra Volume: 印刷中
  • Peer Reviewed
• [Journal Article] Construction of Auslander-Gorenstein local rings as Frobenius extensions (2015)
  • Author(s): M. Hoshino, N. Kameyama and H. Koga
  • Journal Title: Colloq. Math. Volume: 印刷中
  • Peer Reviewed
• [Journal Article] Group-graded and group-bigraded rings (2015)
  • Author(s): M. Hoshino, N. Kameyama and H. Koga
  • Journal Title: J. Algebra Appl. Volume: 印刷中
  • NAID: 120007130256
  • Peer Reviewed
• [Presentation] Artin's problem (2016)
  • Author(s): 古賀寛尚
  • Organizer: 第21 回代数学若手研究会
  • Place of Presentation: 奈良女子大学(奈良県, 奈良市)
  • Year and Date: 2016-03-28
  • Invited
• [Presentation] Derived equivalences and Gorenstein projective dimension (2015)
  • Author(s): Hirotaka Koga
  • Organizer: Derived categories of nite dimensional algebras
  • Place of Presentation: 静岡大学(静岡県, 静岡市)
  • Year and Date: 2015-09-11
  • Int'l Joint Research / Invited
• [Presentation] Crossed products, Frobenius extension, Auslander-Gorenstein ring (2015)
  • Author(s): 亀山統胤・星野光男・古賀寛尚
  • Organizer: 第48回環論および表現論シンポジウム
  • Place of Presentation: 名古屋大学(愛知県, 名古屋市)
  • Year and Date: 2015-09-07
• [Presentation] Derived equivalences and Gorenstein projective dimension (2015)
  • Author(s): 古賀寛尚・星野光男
  • Organizer: 第48回環論および表現論シンポジウム
  • Place of Presentation: 名古屋大学(愛知県, 名古屋市)
  • Year and Date: 2015-09-07
• [Presentation] Derived equivalences and Gorenstein projective dimension (2015)
  • Author(s): 古賀寛尚
  • Organizer: 第60回代数学シンポジウム
  • Place of Presentation: 静岡大学(静岡県, 静岡市)
  • Year and Date: 2015-08-31
  • Invited
• [Presentation] Clifford extensions (2015)
  • Author(s): Mitsuo HOSHINO, Noritsugu KAMEYAMA and Hirotaka KOGA
  • Organizer: THE SEVENTH CHINA-JAPAN-KOREA INTERNATIONAL SYMPOSIUM ON RING THEORY
  • Place of Presentation: Zhejiang University of Technology and Zhejiang University(China)
  • Year and Date: 2015-07-02
  • Int'l Joint Research
• [Presentation] Rings derived equivalent to Z (2015)
  • Author(s): 古賀寛尚
  • Organizer: 2015年度日本数学会年会
  • Place of Presentation: 明治大学(東京都, 千代田区)
  • Year and Date: 2015-03-21 – 2015-03-24
• [Presentation] Rings derived equivalent to Z (2015)
  • Author(s): 古賀寛尚
  • Organizer: 第20回代数学若手研究会
  • Place of Presentation: 名古屋大学(愛知県, 名古屋市)
  • Year and Date: 2015-03-18 – 2015-03-20
• [Presentation] ホモロジー代数的予想とその周辺 (2014)
  • Author(s): 古賀寛尚
  • Organizer: 組合せ論セミナー
  • Place of Presentation: 東北大学(宮城県, 仙台市)
  • Year and Date: 2014-12-26
  • Invited
• [Presentation] Group-graded and group-bigraded rings (2014)
  • Author(s): 星野光男・亀山統胤・古賀寛尚
  • Organizer: 2014年度日本数学会秋季総合分科会
  • Place of Presentation: 広島大学(広島県, 東広島市)
  • Year and Date: 2014-09-25 – 2014-09-28
• [Presentation] On standard derived equivalences (2014)
  • Author(s): 古賀寛尚
  • Organizer: 2014年度日本数学会秋季総合分科会
  • Place of Presentation: 広島大学(広島県, 東広島市)
  • Year and Date: 2014-09-25 – 2014-09-28
• [Presentation] Dualities in stable categories (2014)
  • Author(s): 古賀寛尚・星野光男・亀山統胤
  • Organizer: 第47回環論および表現論シンポジウム
  • Place of Presentation: 大阪市立大学(大阪府, 大阪市)
  • Year and Date: 2014-09-13 – 2014-09-15