Orbifold construction of holomorphic vertex operator algebras associated to inner automorphisms

Abstract

In this article, we construct three new holomorphic vertex operator algebras of central charge $24$ using the ${\mathbb{Z}}_2$-orbifold construction associated to inner automorphisms. Their weight one subspaces has the Lie algebra structures $D_{7,3}{A}_{3,1}{G}_{2,1}$, $E_{7,3}{A}_{5,1}$, and $A_{8,3}{A}_{2,1}^2$. In addition, we discuss the constructions of holomorphic vertex operator algebras with Lie algebras $A_{5,6}{C}_{2,3}{A}_{1,2}$ and $D_{6,5}{A}_{1,1}^2$ from holomorphic vertex operator algebras with Lie algebras $C_{5,3}{G}_{2,2}{A}_{1,1}$ and $A_{4,5}^2$, respectively.

42 pages

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