TY - JOUR

T1 - Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24

AU - Lam, Ching Hung

AU - Shimakura, Hiroki

N1 - Funding Information:
C.H. Lam was partially supported by NSC grant 97-2115-M-006-015-MY3 and National Center for Theoretical Sciences, Taiwan. H. Shimakura was partially supported by Grants-in-Aid for Scientific Research (No. 20549004, No. 23540013) and by Excellent Young Researcher Overseas Visit Program, Japan Society for the Promotion of Science.

PY - 2012/3

Y1 - 2012/3

N2 - In 1993, Schellekens ['Meromorphic c=24 conformal field theories', Comm. Math. Phys. 153 (1993) 159-185.] obtained a list of possible 71 Lie algebras of holomorphic vertex operator algebras with central charge 24. However, not all cases are known to exist. The aim of this article is to construct new holomorphic vertex operator algebras (VOAs) using the theory of framed VOAs and to determine the Lie algebra structures of their weight 1 subspaces. In particular, we study holomorphic framed vertex operator algebras associated to subcodes of the triply even codes RM(1, 4) 3 and RM(1, 4)⊕ (d16 +) of length 48. These VOAs correspond to the holomorphic simple current extensions of the lattice type VOAs and. We determine such extensions using a quadratic space structure on the set of all irreducible modules R(W) of W when or As our main results, we construct seven new holomorphic VOAs of central charge 24 in Schellekens' list and obtain a complete list of all Lie algebra structures associated to the weight 1 subspaces of holomorphic framed VOAs of central charge 24. 2011 London Mathematical Society2011

AB - In 1993, Schellekens ['Meromorphic c=24 conformal field theories', Comm. Math. Phys. 153 (1993) 159-185.] obtained a list of possible 71 Lie algebras of holomorphic vertex operator algebras with central charge 24. However, not all cases are known to exist. The aim of this article is to construct new holomorphic vertex operator algebras (VOAs) using the theory of framed VOAs and to determine the Lie algebra structures of their weight 1 subspaces. In particular, we study holomorphic framed vertex operator algebras associated to subcodes of the triply even codes RM(1, 4) 3 and RM(1, 4)⊕ (d16 +) of length 48. These VOAs correspond to the holomorphic simple current extensions of the lattice type VOAs and. We determine such extensions using a quadratic space structure on the set of all irreducible modules R(W) of W when or As our main results, we construct seven new holomorphic VOAs of central charge 24 in Schellekens' list and obtain a complete list of all Lie algebra structures associated to the weight 1 subspaces of holomorphic framed VOAs of central charge 24. 2011 London Mathematical Society2011

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U2 - 10.1112/plms/pdr041

DO - 10.1112/plms/pdr041

M3 - Article

AN - SCOPUS:84858247497

VL - 104

SP - 540

EP - 576

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

IS - 3

ER -