Holomorphic Vertex Operator Algebras of Small Central Charges
Quantum Algebra
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0203005,
title = {Holomorphic Vertex Operator Algebras of Small Central Charges},
author = {C. Dong and G. Mason},
journal= {arXiv preprint arXiv:math/0203005},
year = {2007}
}
Comments
13 pages, latex