The Rank-2 Lattice-Type Vertex Operator Algebras V_L~+ and Their Automorphism Groups

摘要

This article continues a program to study automorphism groups of vertex operator algebras (VOAs). See references in the survey and the more recent articles. Here we investigate the fixed point subVOA of a lattice-type VOA with respect to a group of order 2 lifting the -1 map on a positive definite lattice. We can obtain a definitive answer for the automorphism group of this subVOA in two extreme cases. The first is where the lattice has no vectors of norm 2 or 4, and the second is where the lattice has rank 2.