Application of a ℤ₃-orbifold construction to the lattice vertex operator algebras associated to Niemeier lattices

2013/02/20 by Daisuke Sagaki, Sagaki, Daisuke, Hiroki Shimakura +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1302.4826

openalex publication_date 2013/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By applying Miyamoto's ℤ₃-orbifold construction to the lattice vertex operator algebras associated to Niemeier lattices and their automorphisms of order 3, we construct holomorphic vertex operator algebras of central charge 24 whose Lie algebras of the weight one spaces are of types A_2,3⁶, E_6,3G_2,1³, and A_5,3D_4,3A_1,1³, which correspond to No.6, No.17, and No.32 on Schellekens' list, respectively.

Related

• Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices
• Automorphism groups of the holomorphic vertex operator algebras associated with Niemeier lattices and the -1-isometries
• On orbifold constructions associated with the Leech lattice vertex operator algebra
• ℤ₂-orbifold construction associated with (-1)-isometry and uniqueness of holomorphic vertex operator algebras of central charge 24
• Orbifold construction and Lorentzian construction of Leech lattice vertex operator algebra