Fourvolutions and automorphism groups of orbifold lattice vertex operator algebras

Hsian-Yang Chen; Ching Hung Lam

paper

Fourvolutions and automorphism groups of orbifold lattice vertex operator algebras

arXiv:2103.07035

Abstract

Let $L$ be an even positive definite lattice with no roots, i.e., $L (2) = {x \in L ∣ (x ∣ x) = 2} = \emptyset$ . Let $g \in O (L)$ be an isometry of order $4$ such that $g^{2} = - 1$ on $L$ . In this article, we determine the full automorphism group of the orbifold vertex operator algebra $V_{L}^{g^}$ . As our main result, we show that $A u t (V_{L}^{g^})$ is isomorphic to $N_{A u t (V_{L})} (⟨ g^⟩) / ⟨ g^⟩$ unless $L ≅ 2 E_{8}$ or $B W_{16}$ .