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We continue our study of cyclic orbifolds of lattice vertex operator algebras and their full automorphism groups. We consider some special isometry $g\in O(L)$ such that $g^i$ is fixed point free on $L$ for any $1\leq i\leq |g|-1$. We show…

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…

We study the fixed point subalgebra of a certain class of lattice vertex operator algebras by an automorphism of order 3, which is a lift of a fixed-point-free isometry of the underlying lattice. We classify the irreducible modules for the…

We determine the automorphism groups of the orbifold vertex operator algebras associated with the coinvariant lattices of isometries of the Leech lattice in the conjugacy classes 3C, 5C, 11A and 23A. These orbifold vertex operator algebras…

The automorphism group of the vertex operator algebra $V_L^+$ is studied by using its action on isomorphism classes of irreducible $V_L^+$-modules. In particular, the shape of the automorphism group of $V_L^+$ is determined when $L$ is…

Given a positive definite even lattice and a commutative ring, there is a standard construction of a lattice vertex algebra over the commutative ring, and it admits a natural grading by non-negative integers. We describe the groups of…

Every isometry $\sigma$ of a positive-definite even lattice $Q$ can be lifted to an automorphism of the lattice vertex algebra $V_Q$. An important problem in vertex algebra theory and conformal field theory is to classify the…

Let $L$ be an even positive definite lattice with no roots, i.e., $L(2)=\{x\in L\mid (x|x)=2\}=\emptyset$. Let $g\in O(L)$ be an isometry of order $4$ such that $g^2=-1$ on $L$. In this article, we determine the full automorphism group of…

In this article, we completely determine the isomorphism classes of lattice vertex operator algebras and the vertex operator subalgebras fixed by a lift of the -1-isometry of the lattice. We also provide similar results for certain even…

Let L be the A_1 root lattice and G a finite subgroup of Aut(V_L), where $V_L$ is the associated lattice VOA (in this case, Aut(V) is isomorphic to PSL(2,\Bbb C)). The fixed point subVOA, V^G was studied in q-alg/9710017, which finds a set…

To a positive-definite even lattice $Q$, one can associate the lattice vertex algebra $V_Q$, and any automorphism $\sigma$ of $Q$ lifts to an automorphism of $V_Q$. In this paper, we investigate the orbifold vertex algebra $V_Q^\sigma$,…

In this article, we determine the automorphism groups of $14$ holomorphic vertex operator algebras of central charge $24$ obtained by applying the $\mathbb{Z}_2$-orbifold construction to the Niemeier lattice vertex operator algebras and…

In this article, we give a method of calculating the automorphism groups of the vertex operator algebras $V_L^+$ associated with even lattices $L$. For example, by using this method we determine the automorphism groups of $V_L^+$ for even…

Let L be a positive definite even lattice of rank one and V_L^+ be the fixed points of the lattice VOA V_L associated to L under an automorphism of V_L lifting the -1$ isometry of L. A set of generators and the full automorphism group of…

We describe the outer automorphism group of a one-ended fundamental group of a graph of groups, when edge groups are cyclic, and vertex groups are torsion-free with cyclic centralizers. We show that in this case the outer automorphism group…

We give a complete description of the full automorphism group of a lattice vertex operator algebra, determine the twisted Zhu's algebra for the automorphism lifted from the -1 isometry of the lattice and classify the corresponding…

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…

We characterize conjugacy classes of isometries of odd prime order in unimodular Z-lattices. This is applied to give a complete classification of odd prime order non-symplectic automorphisms of irreducible holomorphic symplectic manifolds…

Let $V$ be a vertex operator superalgebra and $g=\left(1\ 2\ \cdots k\right)$ be a $k$-cycle which is viewed as an automorphism of the tensor product vertex operator superalgebra $V^{\otimes k}$. In this paper, we construct an explicit…

In this article, we study orbifold constructions associated with the Leech lattice vertex operator algebra. As an application, we prove that the structure of a strongly regular holomorphic vertex operator algebra of central charge $24$ is…