Constructions of the moonshine vertex operator algebra by using orbifold theories

2010 Fiscal Year Self-evaluation Report

• Project/Area Number: 20549004
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Aichi University of Education
• Principal Investigator: SHIMAKURA Hiroki Aichi University of Education, 教育学部, 講師 (90399791)
• Project Period (FY): 2008 – 2011
• Keywords: 頂点作用素代数 / ムーンシャイン / モンスター / 符号 / 格子 / 自己同型群 / 直交群

Research Abstract

ムーンシャイン頂点作用素代数の再構成を軌道体構成法を用いて行う。特に、位数3の自己同型に付随する軌道体構成法によるムーンシャイン頂点作用素代数の構成法を行う。そして、構成法に付随するモンスターの部分群を頂点作用素代数を用いて記述し研究することで、モンスターについての理解を深める。

Research Products

• [Journal Article] An E_8-approach to the moonshine vertex operator algebra (2011)
  • Author(s): H.Shimakura
  • Journal Title: J.London Math.Soc. 83 Pages: 493-516
  • Peer Reviewed
• [Journal Article] Frame Stabilizers for framed vertex operator algebras associated to lattices having 4-frames (2009)
  • Author(s): C.H. Lam, H.Shimakura
  • Journal Title: Int.Math.Res.Not.IMRN Pages: 4547-4577
  • Peer Reviewed
• [Journal Article] Even lattices obtained from doubly even codes and VOAs obtained fromeven lattices (2009)
  • Author(s): 島倉裕樹
  • Journal Title: 数理解析研究所講究録 1656 Pages: 74-83
• [Presentation] Toward the classification of holomorphic framed vertex operator algebras of central charge 24 (2010)
  • Author(s): 島倉裕樹
  • Organizer: 頂点作用素代数・有限群・組合せ論の研究
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 20101200
• [Presentation] Toward the classification of holomorphic framed vertex operator algebras of central charge 24 (2010)
  • Author(s): H. Shimakura
  • Organizer: Mini-Workshop on infinite dimensional Lie algebras and related topics
  • Place of Presentation: National Cheng Kung University
  • Year and Date: 20100900
• [Presentation] Quadratic spaces and the moonshine vertex operator algebra (2010)
  • Author(s): H. Shimakura
  • Organizer: The 8th Korea-Japan Workshop on Algebra and Combinatorics
  • Place of Presentation: POSTECH
  • Year and Date: 20100200
• [Presentation] An $E_8$ approach to the moonshine vertex operator algebra (2009)
  • Author(s): H.Shimakura
  • Organizer: One day workshop on algebraic combinatrices
  • Place of Presentation: Academia sinica
  • Year and Date: 20091000
• [Presentation] Even lattices obtained from doubly even codes and VOAs obtained from even lattices (2009)
  • Author(s): 島倉裕樹
  • Organizer: 有限群・頂点作用素代数と組合せ論
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 20090100