Ching Hung Lam

Academia Sinica

Automorphism groups of cyclic orbifolds of lattice VOA

Algebra Seminar

20th June 2022, 4:00 pm – 5:00 pm
Fry Building, Room 2.04

Let V be a vertex operator algebra (VOA) and g∈Aut(V) a finite automorphism of V.The fixed point subset Vg = { xV | 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 NAut(V)(⟨g⟩) acts on the fixed point space Vg. Therefore, the main question is to determine if there are automorphisms which are not induced from NAut(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.

Organisers: Tim Burness, Charles Cox

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