Study on structures and representations of Cartan type Lie superalgebras from view point of mathematical physics

• Project/Area Number: 18740005
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: University of Fukui
• Principal Investigator: KOGA Yoshiyuki University of Fukui, 大学院工学研究科, 准教授 (20338429)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥2,710,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥210,000); Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000); Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
• Keywords: 代数一般 / 超ヴィラソロ代数 / 特異ベクトル公式 / 特異ベクトル

Research Abstract

本研究は、無限次元カルタン型超リー代数(コンファーマル超代数)の表現論を主な研究対象とした。無限次元カルタン型超リー代数は、ヴィラソロ代数と呼ばれる最も重要な無限次元リー代数を含む超リー代数で、その表現論は、共形場の理論等の数理物理学において様々な応用をもつ。本研究では、最も基本的な無限次元カルタン型超リー代数であるN=1超ヴィラソロ代数の表現論やその数理物理学への応用を中心に研究を行い、特にN=1超ヴィラソロ代数のフュージョン代数(共形場理論から定まる代数)の構造に関する結果などを得た。

Research Products

• [Journal Article] Fusion algebras for N=1 superconformal field theories through coinvariants II+1/2 : Ramond sector (2009)
  • Author(s): K Iohara, Y. Koga
  • Journal Title: International Mathematics Research Notices (印刷中)
  • Peer Reviewed
• [Journal Article] The structure of pre-Verma modules over the N=1 Ramond algebra (2006)
  • Author(s): K Iohara, Y. Koga
  • Journal Title: Letter in Mathematical Physics 78 Pages: 89-96
  • Peer Reviewed
• [Journal Article] Tilting equivalence for superconformal algebras (2006)
  • Author(s): K Iohara, Y. Koga
  • Journal Title: Mathematica Scandinavica 99 Pages: 17-52
  • Peer Reviewed
• [Journal Article] The structure of pre-Verma modules over the N=1 Ramond algebra (2006)
  • Author(s): K.lohara, Y.Koga
  • Journal Title: Lett. Math. Phys. 78 Pages: 89-96
• [Journal Article] Tilting equivalence for superconformal algebras (2006)
  • Author(s): K.lohara, Y.Koga
  • Journal Title: Math. Scand. 99 Pages: 17-52
• [Journal Article] Fusion Algebras for N=1 Superconformal Field Theories through Coinvariants ll+ 1/2 : Ramond Sector
  • Author(s): K. Iohara, Y. Koga
  • Journal Title: Int. Math. Res. Notice (印刷中)
  • Peer Reviewed
• [Presentation] Fusion algebras for N=1 super Virasoro algebras (2008)
  • Author(s): Yoshiyuki Koga
  • Organizer: 研究集会Algebras, Groups and Geometries
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2008-12-11
• [Presentation] Fusion algebras for N=1 super Virasoro algebras (2008)
  • Author(s): Y. Koga
  • Organizer: 研究集会「Algebras, Groups and Geometries 2008」
  • Place of Presentation: 東京大学数理科学研究科
• [Presentation] Singular vector formula for Kac-Moody Lie(super)algebras (2007)
  • Author(s): 古閑義之
  • Organizer: 研究集会Vertex algebra in Tambara
  • Place of Presentation: 東京大学玉原セミナーハウス
  • Year and Date: 2007-08-15
• [Presentation] Singular vector formula for Kac-Moody Lie (super)algebras (2007)
  • Author(s): Y. Koga
  • Organizer: 研究集会 Vertex algebra in Tambara
  • Place of Presentation: 東京大学玉原セミナーハウス