TY - JOUR

T1 - On orbifold constructions associated with the Leech lattice vertex operator algebra

AU - Lam, Ching Hung

AU - Shimakura, Hiroki

N1 - Funding Information:
† Partially supported by MoST grant 104-2115-M-001-004-MY3 of Taiwan. ‡ Partially supported by JSPS KAKENHI Grant Numbers JP26800001 and JP17K05154. § Both authors were partially supported by JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers “Development of Concentrated Mathematical Center Linking to Wisdom of the Next Generation”.

PY - 2020/3/1

Y1 - 2020/3/1

N2 - In this paper, we study orbifold constructions associated with the Leech lattice vertex operator algebra. As an application, we prove that the structure of a strongly regular holomorphic vertex operator algebra of central charge 24 is uniquely determined by its weight one Lie algebra if the Lie algebra has the type A3,43A1,2, A4,52, D4,12A2,6, A6,7, A7,4A1,13, D5,8A1,2 or D6,5A1,12 by using the reverse orbifold construction. Our result also provides alternative constructions of these vertex operator algebras (except for the case A6,7) from the Leech lattice vertex operator algebra.

AB - In this paper, we study orbifold constructions associated with the Leech lattice vertex operator algebra. As an application, we prove that the structure of a strongly regular holomorphic vertex operator algebra of central charge 24 is uniquely determined by its weight one Lie algebra if the Lie algebra has the type A3,43A1,2, A4,52, D4,12A2,6, A6,7, A7,4A1,13, D5,8A1,2 or D6,5A1,12 by using the reverse orbifold construction. Our result also provides alternative constructions of these vertex operator algebras (except for the case A6,7) from the Leech lattice vertex operator algebra.

UR - http://www.scopus.com/inward/record.url?scp=85052877798&partnerID=8YFLogxK

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U2 - 10.1017/S0305004118000658

DO - 10.1017/S0305004118000658

M3 - Article

AN - SCOPUS:85052877798

VL - 168

SP - 261

EP - 285

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 2

ER -