Automorphism groups and uniqueness of holomorphic vertex operator algebras of central charge $24$

Abstract

We describe the automorphism groups of all holomorphic vertex operator algebras of central charge $24$ with non-trivial weight one Lie algebras by using their constructions as simple current extensions. We also confirm a conjecture of G. Höhn on the numbers of holomorphic vertex operator algebras of central charge $24$ obtained as inequivalent simple current extensions of certain vertex operator algebras, which gives another proof of the uniqueness of holomorphic vertex operator algebras of central charge $24$ with non-trivial weight one Lie algebras.

arXiv comment45 pages, some typo in Genus A of Table 26 are corrected in the version v3

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• Modular invariance of trace functions in orbifold theory
• Meromorphic c=24 Conformal Field Theories
• C_2-cofiniteness of cyclic-orbifold models
• Construction and Classification of Holomorphic Vertex Operator Algebras
• Schur-Weyl Duality for Heisenberg Cosets
• Certain extensions of vertex operator algebras of affine type
• Gluing vertex algebras
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Cited by in corpus (6)

• Bosonic Rational Conformal Field Theories in Small Genera, Chiral Fermionization, and Symmetry/Subalgebra Duality
• Haploid algebras in $C^{\ast }$-tensor categories and the Schellekens list
• Two-dimensional conformal field theory, full vertex algebra and current-current deformation
• Unitarity and strong graded locality of holomorphic vertex operator superalgebras with central charge at most 24
• A Geometric Classification of the Holomorphic Vertex Operator Algebras of Central Charge 24
• Automorphism groups of certain orbifold vertex operator algebras arising from coinvariant lattices associated with the Leech lattice