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Research and Construction of Vertex Operator Algebras of finite type

Research Project

Project/Area Number 22340002
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionUniversity of Tsukuba

Principal Investigator

MIYAMOTO MASAHIKO  筑波大学, 数理物質系, 教授 (30125356)

Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥16,250,000 (Direct Cost: ¥12,500,000、Indirect Cost: ¥3,750,000)
Fiscal Year 2013: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2012: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2011: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2010: ¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Keywords頂点作用素代数 / 自己同型 / C2有限性 / 軌道理論 / 軌道構成 / ホロモルフィック頂点作用素代数 / ムーンシャイン頂点作用素代数 / モンスター単純群 / 有限自己同型群 / C2余有限 / 有理型 / シンプルカレント構成 / 2次元共形場理論 / C2有限性 / フュージョン積 / C1有限性 / ムーンシャイン予想 / フレイム頂点作用素代数 / 2次元共形場理論 / C1有限性 / 置換頂点作用素代数 / オービフォルド理論 / 格子頂点作用素代数
Research Abstract

One of important problem on Conformal Field Theory (Vertex Operator Algebra) is to construct one of finite type. One of the candidates to construct one of finite type is an orbifold theory using a finite automorphism group, but it is not easy to treat. In this research, we succeed to prove the hereditary of C2-cofiniteness under the orbifold theory for a finite cyclic automorphism, which is the main purpose of this research. By this result, an orbifold construction of holomorphic vertex operator algebras becomes problems to check the weights and fusion rules. As application, several researchers succeeded to construct new holomorphic vertex operator algebra using this result.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (23 results)

All 2013 2012 2011 2010 Other

All Journal Article (6 results) (of which Peer Reviewed: 6 results) Presentation (15 results) (of which Invited: 3 results) Book (2 results)

  • [Journal Article] C_1-Cofiniteness and Fusion Products for Vertex Operator Algebras2013

    • Author(s)
      Masahiko Miyamoto
    • Journal Title

      Conformal Field Tehories and Tensor Categories

      Volume: 1 Pages: 271-279

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Z3-orbifold theory of lattice vertex operator algebra and Z3-orbifold construction2013

    • Author(s)
      Masahiko Miyamoto
    • Journal Title

      Symmetries, Integrable Systems and Representation

      Volume: 1 Pages: 319-344

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Z_3-orbifold theory of lattice vertex operator algebra and Z3-orbifold construction, Symmetries2012

    • Author(s)
      Masahiko Miyamoto
    • Journal Title

      Integrable Systems and Representation

      Volume: Vol.364 Pages: 88-89

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Non-vanishing elements in finite groups2012

    • Author(s)
      Masahiko Miyamoto
    • Journal Title

      Journal of Algebra

      Volume: Vol.364 Pages: 88-89

    • NAID

      120007137284

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on a conjecture of K. Harada and strongly p-embedded Frobenius subgroups2010

    • Author(s)
      Masahiko Miyamoto, Koichiro Harada
    • Journal Title

      Journal of Group Theory

      Volume: Vol.13 Pages: 469-475

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Anote on a conjecture of K. Harada and strongly p-embedded Frobenius subgroups.2010

    • Author(s)
      宮本雅彦 K.Harada
    • Journal Title

      J.Group Theory

      Volume: 13 Pages: 469-475

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Z2-orbifold theory of vertex operato algebra2013

    • Author(s)
      Masahiko Miyamoto
    • Organizer
      Group theory, VOA and Algebraic combinatorics
    • Place of Presentation
      台東大学(台湾国立中央研究院と台南大学主催)(中華民国)
    • Year and Date
      2013-03-25
    • Related Report
      2013 Final Research Report
  • [Presentation] On Z2-orbifold theory of vertex operator algebra2013

    • Author(s)
      Masahiko Miyamoto
    • Organizer
      Group theory, VOA and Algebraic combinatorics
    • Place of Presentation
      台東大学(台湾)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Z3-orbifold construction of vertex operator algebras2011

    • Author(s)
      Masahiko Miyamoto
    • Organizer
      Conference on vertex operator algebras, finite groups and related topics
    • Place of Presentation
      Academia Sinica(台湾)(招待講演)
    • Year and Date
      2011-12-21
    • Related Report
      2011 Annual Research Report
  • [Presentation] Z3-orbifold construction of vertex operator algebras2011

    • Author(s)
      Masahiko Miyamoto
    • Organizer
      Symmetries, integrable systems and representations
    • Place of Presentation
      リオン第4大学(フランス)
    • Year and Date
      2011-12-13
    • Related Report
      2013 Final Research Report
  • [Presentation] C2-cofiniteness of VOAs and orbifold theory2011

    • Author(s)
      Masahiko Miyamoto
    • Organizer
      Symmetries, integrable systems and representations
    • Place of Presentation
      リオン第4大学(フランス)(招待講演)
    • Year and Date
      2011-12-13
    • Related Report
      2011 Annual Research Report
  • [Presentation] Z3-orbifold construction of vertex operator algebras2011

    • Author(s)
      Masahiko Miyamoto
    • Organizer
      Conference on vertex operator algebras, finite groups and related topics
    • Place of Presentation
      Academia Sinica 台湾国立中央研究院(中華民国)
    • Year and Date
      2011-11-21
    • Related Report
      2013 Final Research Report
  • [Presentation] Z_3-oribifold construction, Conformal Field Theory2011

    • Author(s)
      Masahiko Miyamoto
    • Organizer
      Automorphic Forms and Related Topics
    • Place of Presentation
      University of Heidelberg(ドイツ)
    • Year and Date
      2011-09-19
    • Related Report
      2013 Final Research Report
  • [Presentation] Z3-oribifold construction2011

    • Author(s)
      Masahiko Miyamoto
    • Organizer
      Conformal Field Theory, Automorphic Forms and Related Topics
    • Place of Presentation
      University of Heidelberg(ドイツ)(招待講演)
    • Year and Date
      2011-09-19
    • Related Report
      2011 Annual Research Report
  • [Presentation] 巡回置換軌道理論と格子頂点作用素代数の軌道理論との関係2011

    • Author(s)
      Masahiko Miyamoto
    • Organizer
      第23回有限群論草津セミナー
    • Place of Presentation
      草津セミナーハウス
    • Year and Date
      2011-07-31
    • Related Report
      2013 Final Research Report
  • [Presentation] C2-cofiniteness of permutation orbifold models and orbifold models of lattice VOAs2011

    • Author(s)
      Masahiko Miyamoto
    • Organizer
      Conformal field theories and tensor categories
    • Place of Presentation
      Beijing International Center (中華人民共和国)
    • Year and Date
      2011-06-14
    • Related Report
      2013 Final Research Report
  • [Presentation] C2-cofiniteness of permutation orbifold models and orbifold modesl of lattice VOAs2011

    • Author(s)
      Masahiko Miyamoto
    • Organizer
      Conformal field theories and tensor categories
    • Place of Presentation
      Beijing international center(中国)(招待講演)
    • Year and Date
      2011-06-14
    • Related Report
      2011 Annual Research Report
  • [Presentation] Orbifold theory of vertex operator algebras.2010

    • Author(s)
      宮本雅彦
    • Organizer
      RIM研究集会
    • Place of Presentation
      京都大学(招待講演)
    • Year and Date
      2010-12-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] Oribifold theory of vertex operator algebras2010

    • Author(s)
      Masahiko Miyamoto
    • Organizer
      Research into Vertex Operator Algebras, Finite Groups and Combinatorics
    • Place of Presentation
      RIMS 京都大学数理解析研究所
    • Year and Date
      2010-12-13
    • Related Report
      2013 Final Research Report
  • [Presentation] Orbifold conjecture for cyclic automorphism

    • Author(s)
      Masahiko Miyamoto
    • Organizer
      Majorana Theory, the Monster and Beyon
    • Place of Presentation
      Imperial colledge London, UK
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 頂点作用素代数に関する軌道予想について

    • Author(s)
      Masahiko Miyamoto
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      愛媛大学(松山市)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Book] 数学の道しるべ2011

    • Author(s)
      宮本雅彦
    • Publisher
      サイエンス社
    • Related Report
      2013 Final Research Report
  • [Book] 数学の道しるべ2011

    • Author(s)
      宮本雅彦(分筆)
    • Publisher
      サイエンス社
    • Related Report
      2011 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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