The automorphism group of the Z_2-orbifold of the Barnes-Wall lattice vertex operator algebra of central charge 32

Abstract

In this article, we prove that the full automorphism group of the Z_2-orbifold of the Barnes-Wall lattice vertex operator algebra of central charge 32 has the shape $2^{27}.E_6(2)$. In order to identify the group structure, we introduce a graph structure on the Griess algebra and show that it is a rank 3 graph associated to $E_6(2)$.

19 pages

References in corpus (1)

• An $E_8$-approach to the moonshine vertex operator algebra

Cited by in corpus (2)

• Curiosities above c = 24
• Classification of extremal vertex operator algebras with two simple modules