### 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 *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.

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