Holomorphic vertex operator algebras of small central charge
By C. Dong, Geoffrey Mason. 2002
99 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/7d974181db42cdcb50ea26bb6a72094f848d9bcb
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In Algebra and Number Theory
- D. Nikshych
- Alexei Davydov
- V. Ostrik
- Michael Mueger
- D. Venku Naidu
- Geoffrey Mason
- C. Dong
- Liang Kong
In Geometry and Topology
- D. Nikshych
- Alexei Davydov
- V. Ostrik
- Michael Mueger
- D. Venku Naidu
- Geoffrey Mason
- C. Dong
- Liang Kong
In Statistical and Nonlinear Physics
- D. Nikshych
- Alexei Davydov
- Michael Mueger
- Geoffrey Mason
- V. Ostrik
- C. Dong
- D. Venku Naidu
- N. Andruskiewitsch
Citations in the corpus
- Integrability of C2-cofinite vertex operator algebras (2006, background): “Remark 4.4 The integrality of the levels ki was already announced at the end of [ DM3 ].”
- Rational vertex operator algebras and the effective central charge (2002, unknown): “VL where L is now a Niemeier lattice (including the Leech Lattice). Thus the special case c = 24 of Corollary 4 confirms with mathematical rigor the completeness of this part of Schellekens’ list. See [DM2] for further developments of this idea. Although there is no mention of modular-invariance in a”
- The Witt group of non-degenerate braided fusion categories (2010, background): “ has infinite order. 6.5. Holomorphic vertex algebras with c= 24. We recallthat a rationalvertex algebra V is called holomorphic if Rep(V) = Vec, that is the only simple V−module is V itself, see e.g. [DM]. In [Sc] Schellekens gives a conjectural list of 71 holomorphic vertex algebras with central ch”