On Majorana representations of the group $3^2:2$ of 3C-pure type and the corresponding vertex operator algebras

Abstract

In this article, we study Griess algebras and vertex operator subalgebras generated by Ising vectors in a moonshine type VOA such that the subgroup generated by the corresponding Miyamoto involutions has the shape $3^2:2$ and any two Ising vectors generate a 3C subVOA $U_{3C}$. We show that such a Griess algebra is uniquely determined, up to isomorphisms. The structure of the corresponding vertex operator algebra is also discussed. In addition, we give a construction of such a VOA inside the lattice VOA $V_{E_8^3}$, which gives an explicit example for Majorana representations of the group $3^2:2$ of 3C-pure type.

References in corpus (3)

• The structure of parafermion vertex operator algebras
• $E{E}_8$-lattices and dihedral groups
• McKay's observation and vertex operator algebras generated by two conformal vectors of central charge 1/2

Cited by in corpus (1)

• A Holomorphic vertex operator algebra of central charge 24 with weight one Lie algebra $F_{4,6}{A}_{2,2}$