Automorphism group schemes of lattice vertex operator algebras

Abstract: Given a positive definite even lattice and a commutative ring, there is a standard construction of a lattice vertex algebra over the commutative ring, and this is promoted to a vertex operator algebra when the determinant of the lattice is invertible. We describe the groups of automorphisms of these vertex algebras and vertex operator algebras as affine group schemes, showing in particular that each is an extension of an explicitly described split reductive group of ADE type by the outer automorphism group of the lattice.