Holomorphic vertex operator algebras of small central charge

Chongying Dong and Geoffrey Mason

Vol. 213 (2004), No. 2, 253–266

DOI: 10.2140/pjm.2004.213.253

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.

Milestones

Received: 18 March 2002

Revised: 1 April 2003

Published: 1 February 2004