A Cyclic Orbifold Theory for Holomorphic Vertex Operator Algebras and Applications

Understand

In this thesis we develop an orbifold theory for a finite, cyclic group $G$ acting on a suitably regular, holomorphic vertex operator algebra $V$.

• To this end we describe the fusion algebra of the fixed-point vertex operator subalgebra $V^G$ and show that $V^G$ has group-like fusion.
• Then we solve the extension problem for vertex operator algebras with group-like fusion.
• We use these results to construct five new holomorphic vertex operator algebras of central charge 24 as lattice orbifolds, contributing to the classification of the $V_1$-structures of suitably regular, holomorphic vertex operator algebras of central charge 24.