Automorphism groups of certain cyclic orbifolds of lattice VOA

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Let $V$ be a VOA and $g\in Aut(V)$ a finite automorphism of $V$. The fixed point subset $V^{\langle g\rangle}= \{x\in V| gx=x\}$ is a subVOA of $V$ and is often called a cyclic orbifold of $V$. In this talk, we will discuss the full automorphism groups of certain cyclic orbifolds of lattice VOA. In particular, we will determine the full automorphism group of some orbifold VOA $V_{\Lambda_g}^g$ associated with coinvariant lattices of the Leech lattice $\Lambda$. As an application, we will determine the full automorphism groups of several holomorphic VOAs of central charge 24.