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2010 Fiscal Year Final Research Report

Study on finiteness properties of vertex operator algebras

Research Project

  • PDF
Project/Area Number 20740017
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionEhime University

Principal Investigator

ABE Toshiyuki  Ehime University, 理工学研究科, 准教授 (30380215)

Project Period (FY) 2008 – 2010
Keywords頂点作用素代数 / 代数 / オービフォールド
Research Abstract

I have been working on a finiteness property called a C_2-cofiniteness property, for a vertex operator algebras. A fixed point subalgebra of a vertex operator algebra by its finite automorphism group is called an orbifold model. In the representation theory of vertex operator algebra there is a conjecture that if a vertex operator algebra has the C_2-cofiniteness property then so does any orbifold model of it. I have found necessary and sufficient conditions which make the conjecture true for commutative vertex algebras and Z_2-permutation orbifold models of vertex operator algebras. I also showed that Z_2-permutation orbifold models of the Virasoro vertex operator algebras having C_2-cofinittness property satisfy the C_2-cofiniteness condition.

  • Research Products

    (8 results)

All 2011 2010 2009 2008

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (7 results)

  • [Journal Article] C2-cofiniteness of the 2-cycle permutation orbifold models of minimal Virasoro vertex operator algebras2011

    • Author(s)
      安部利之
    • Journal Title

      Communications in Mathematical Physics 303, Issue3

      Pages: 825-844

    • Peer Reviewed
  • [Presentation] On C2-cofiniteness of Z2-permutation orbifold models2010

    • Author(s)
      安部利之
    • Organizer
      頂点作用素代数,群論,組合せ論
    • Place of Presentation
      京都大学
    • Year and Date
      2010-12-16
  • [Presentation] On C2-cofiniteness of 2-cycle permutation orbifold models of the Virasoro VOAs2010

    • Author(s)
      安部利之
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-22
  • [Presentation] 可換頂点代数のZN-オービフォールド模型のC2有限性について2009

    • Author(s)
      安部利之
    • Organizer
      日本数学会秋期総合分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
  • [Presentation] On C2-cofinteness of vertex operator algebras,Algebras2009

    • Author(s)
      安部利之
    • Organizer
      Groups and Geometries 2009 in Tambara
    • Place of Presentation
      群馬県東京大学丹原セミナーハウス
    • Year and Date
      2009-08-21
  • [Presentation] 可換頂点代数のオービフォールド模型のC2有限性について2009

    • Author(s)
      安部利之
    • Organizer
      第21回草津セミナー
    • Place of Presentation
      群馬県草津セミナーハウス
    • Year and Date
      2009-08-03
  • [Presentation] On C2-cofiniteness of Z2-orbifold models of vertex operator algebras2009

    • Author(s)
      安部利之
    • Organizer
      有限群・頂点作用素代数と組合せ論
    • Place of Presentation
      京都大学
    • Year and Date
      2009-01-06
  • [Presentation] On representation theory for the symplectic-fermionic vertex operator superalgebra2008

    • Author(s)
      安部利之
    • Organizer
      Algebras, Groups and Geometries 2008
    • Place of Presentation
      東京大学
    • Year and Date
      2008-12-10

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Published: 2012-02-13   Modified: 2018-10-23  

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