Ching Hung Lam

Automorphism groups of cyclic orbifolds of lattice VOA

Let V be a vertex operator algebra (VOA) and g∈Aut(V) a finite automorphism of V.The fixed point subset V^⟨g⟩ = { x∈V | gx=x } is a vertex subalgebra of V and is often called a cyclic orbifold of V. In this talk, we will discuss some general methods for computing the full automorphism groups of cyclic orbifolds of lattice VOA.

It is clear that N_Aut(V)(⟨g⟩) acts on the fixed point space V^⟨g⟩. Therefore, the main question is to determine if there are automorphisms which are not induced from N_Aut(V)(⟨g⟩). We will discuss a method to construct such kinds of “extra” automorphisms. As examples, we will determine the full automorphism groups of some orbifold VOA associated with some coinvariant lattices of the Leech lattice.

I will keep the technical details about VOA to a minimum and make it accessible to group theorists or algebraists.