Cyclic orbifolds of lattice vertex operator algebras having group-like fusions

• Published in: Letters in mathematical physics Vol. 110; no. 5; pp. 1081 - 1112
• Main Author: Lam, Ching Hung
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.05.2020; Springer Nature B.V
• Subjects: Algebra; Complex Systems; Geometry; Group Theory and Generalizations; Lattices (mathematics); Mathematical analysis; Mathematical and Computational Physics; Physics; Physics and Astronomy; Subgroups; Theoretical; Cyclic orbifold; Group-like fusion; Secondary 11H56; Primary 17B69; Vertex operator algebra; Leech lattice
• ISSN: 0377-9017; 1573-0530
• DOI: 10.1007/s11005-019-01251-2

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 ^ .