Holomorphic Vertex Operator Algebras of Small Central Charges

2002/03/01 by C. Dong, Chongying Dong, Dong, C. +3 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/0203005

13 pages, latex

arxiv created 2002/03/01 · openalex publication_date 2002/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a rigorous mathematical foundation to the study of strongly rational, holomorphic vertex operator algebras V of central charge c = 8, 16 and 24 initiated by Schellekens. If c = 8 or 16 we show that V is isomorphic to a lattice theory corresponding to a rank c even, self-dual lattice. If c = 24 we prove, among other things, that either V is isomorphic to a lattice theory corresponding to a Niemeier lattice or the Leech lattice, or else the Lie algebra on the weight one subspace V₁ is semisimple (possibly 0) of Lie rank less than 24.

Citations

• Symmetric invariant bilinear forms on vertex operator algebras
• Local systems of vertex operators, vertex superalgebras and modules

Cited by

• Haagerup Symmetry in (E₈)₁?

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• A characterization of vertex operator algebras V_Zα⁺: I
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