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Subalgebras of lattice vertex operator algebras

Research Project

Project/Area Number 13640012
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionHitotsubashi University

Principal Investigator

YAMADA Hiromichi  Hitotsubashi University, Graduate School of Economics, Professor, 大学院・経済学研究科, 教授 (50134888)

Project Period (FY) 2001 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2002: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2001: ¥800,000 (Direct Cost: ¥800,000)
Keywordsvertex operator algebra / Virasoro algebra / conformal vector / highest weight vector / moonshine module / orbifold
Research Abstract

The structure of vertex operator algebra associated with a lattice L which is √<2> times an ordinary root lattice of type A, D, or E was studied. In 2001, the decomposition of the lattice vertex operator algebra into a direct sum of irreducible modules for a subalgebra generated by mutually orthogonal conformal vectors was studied.
1. In the case L = √<2A>_1, all highest weight vectors of weight at most 2 are determined.
2. In the case L= √<2D>_1, all highest weight vectors are determined for a certain choice of conformal vectors.
3. Using the case L = √<2A>_3, a new type of vertex operator algebras are constructed from Z_8 codes.
4. A complete decomposition of the moonshine module as a module for a certain vertex operator algebra related to the case L = √<2A>_3 is obtained.
In 2002, the orbifold for an automorphism of order 3 was studied.
5. The W_3 algebra of central charge 6/5 is discovered as a subalgebra of the orbifold of the lattice vertex operator algebra of type √<2A>_2.

Report

(3 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • Research Products

    (23 results)

All Other

All Publications (23 results)

  • [Publications] H.Yamada: "Highest weight vectors with small weights in the vertex operator algebra associated with a lattice of type √2A_1"Communications in Algebra. 29. 1311-1324 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] C.Dong, C.H.Lam, H.Yamada: "Decomposition of the vertex operator algebra V_{√2D_1}"Communications in Contemporary Mathematics. 3. 137-151 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M.Kiazume, C.H.Lam, H.Yamada: "A class of vertex operator algebras constructed from Z_8 codes"Journal of Algebra. 242. 338-359 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M.Kiazume, C.H.Lam, H.Yamada: "Moonshine vertex operator algebra as L(1/2,0)×L(7/10)XL(4/5,0)×L(1,0)-modules"Journal of Pure and Applied Algebra. 173. 15-48 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H.Yamada: "Highest weight vectors in the vertex operator algebra associated with a lattice of type√2D_1"Communications in Algebra. 30. 5065-5089 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] C.H.Lam, H.Yamada: "Z_3 twisted representations of lattice vertex operator algebras"Communications in Algebra. 31. 3001-3020 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M.Kiazume, C.H.Lam, H.Yamada: "3-State Potts model, moonshine vertex operator algebra and 3A-elements of the monster group"International Mathematics Research Notices. 23. 1269-1303 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H. Yamada: "Highest weight vectors with small weights in the vertex operator algebra associated with a lattice of type √<2A>_1"Communications in Algebra. 29. 1311-1324 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] C. Dong, C. H. Lam, H. Yamada: "Decomposition of the vertex operator algebra V_{√<2D>_1}"Communications in Contemporary Mathematics. 3. 137-151 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M. Kitazume, C. H. Lam, H. Yamada: "A class of vertex operator algebras constructed from Z_8 code"Journal of Algebra. 242. 338-359 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M. Kitazume, C. H. Lam, H. Yamada: "Moonshine vertex operator algebra as L(1/2,0)×L(7/10,0)×L(4/5,0)×L(1,0)-modules"Journal of Pure and Applied Algebra. 173. 15-48 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H. Yamada: "Highest weight vectors in the vertex operator algebra associated with a lattice of type √<2D>_1"Communications in Algebra. 30. 5065-5089 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] C. H. Lam, H. Yamada: "Z_3-twisted representations of lattice vertex operator algebras"Communications in Algebra. 31. 3001-3020 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M. Kitazume, C. H. Lam, H. Yamada: "3-State Potts model, moonshine vertex operator algebra and 3A-elements of the monster group"International Mathematics Research Notices. 23. 1269-1303 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M.Kitazume, C.H.Lam, H.Yamada: "Moonshine vertex operator algebra as L(1/2,0)×L(7/10)×L(4/5,0)-modules"Journal of Pure and Applied Algebra. 173. 15-48 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] H.Yamada: "Highest weight vectors in the vertex operator algebra associated with a lattice of type √2D_1"Communications in Algebra. 30. 5065-5089 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] C.H.Lam, H.Yamada: "Z_3-twisted representations of lattice vertex operator algebras"Communications in Algebra. (発表予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Kitazume, C.H.Lam, H.Yamada: "3-State Potts model, moonshine vertex operator algebra and 3A-elements of the monster group"International Mathematics Research Notices. (発表予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] H.Yamada: "Highest weight vectors with small weights in the vertex operator algebra associated with a lattice of type √2 A_1"Communications in Algebra. 29. 1311-1324 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] C.Dong, C.H.Lam, H.Yamada: "Decomposition of the vertex operator algebra V_{√2D_1}"Communications in Contemporary Mathematics. 3. 137-151 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] M.Kitazume, C.H.Lam, H.Yamada: "A class of vertex operator algebras constructed from Z_8 codes"Journal of Algebra. 242. 338-359 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] M.Kitazume, C.H.Lam, H.Yamada: "Moonshine vertex operator algebra as L(1/2, 0)×L(7/10, 0)×L(4/5, 0)×L(1, 0)-module"Journal of Pure and Applied Algebra. (発表予定,未定).

    • Related Report
      2001 Annual Research Report
  • [Publications] H.Yamada: "Highest weight vectors in the vertex operator algebra associated with a lattice of type √2 D_1"Communications in Algebra. (発表予定,未定).

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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