Automorphism groups of cyclic orbifold vertex operator algebras associated with the Leech lattice and some non-prime isometries

TL;DR

This paper determines the automorphism groups of specific cyclic orbifold vertex operator algebras related to the Leech lattice, providing insights into their symmetries and aiding the classification of holomorphic VOAs of central charge 24.

Contribution

It explicitly computes automorphism groups for orbifold VOAs associated with certain non-prime isometries of the Leech lattice, extending previous classifications.

Findings

Automorphism groups for orbifold VOAs in classes 4C, 6E, 6G, 8E, 10F are determined.

Complete automorphism groups for all 10 VOAs in a referenced classification are identified.

Results facilitate analysis of holomorphic VOAs with central charge 24.

Abstract

We determine the automorphism groups of the cyclic orbifold vertex operator algebras associated with coinvariant lattices of isometries of the Leech lattice in the conjugacy classes $4C,6E,6G,8E$ and $10F$. As a consequence, we have determined the automorphism groups of all the $10$ vertex operator algebras in [H\"o], which are useful to analyze holomorphic vertex operator algebras of central charge $24$.