Cyclic orbifolds of lattice vertex operator algebras having group-like fusions - Lam, Ching Hung (Letters in mathematical physics, 2020)
Let L be an even (positive definite) lattice and g ∈ O ( L ) . In this article, we prove that the orbifold vertex operator algebra V L g ^ has group-like fusion if and only if g acts trivially on the discriminant group D ( L ) = L ∗ / L (or equivalently ( 1 - g ) L ∗ < L ). We also determine their fusion rings and the corresponding quadratic space structures when g is fixed point free on L . By applying our method to some coinvariant sublattices of the Leech lattice Λ , we prove a conjecture proposed by G. Höhn. In addition, we also discuss a construction of certain holomorphic vertex operator algebras of central charge 24 using the orbifold vertex operator algebra V Λ g g ^ .