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 -