Holomorphic Vertex Operator Algebras of Small Central Charges

DOI10.2140/PJM.2004.213.253arXivmath/0203005MaRDI QIDQ6471695

Publication date: 28 February 2002

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 V_1 is semisimple (possibly 0) of Lie rank less than 24.

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Relationship to Lie algebras and finite simple groups (11F22) Vertex operators; vertex operator algebras and related structures (17B69)

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