# Twisted Modules over Lattice Vertex Algebras

@article{Bakalov2004TwistedMO, title={Twisted Modules over Lattice Vertex Algebras}, author={Bojko Bakalov and Victor G. Kac}, journal={arXiv: Quantum Algebra}, year={2004} }

For any integral lattice $Q$, one can construct a vertex algebra $V_Q$ called a lattice vertex algebra. If $\sigma$ is an automorphism of $Q$ of finite order, it can be lifted to an automorphism of $V_Q$. In this paper we classify the irreducible $\sigma$-twisted $V_Q$-modules. We show that the category of $\sigma$-twisted $V_Q$-modules is a semisimple abelian category with finitely many isomorphism classes of simple objects.

## 67 Citations

### Twisted logarithmic modules of free field algebras

- Mathematics
- 2016

Given a non-semisimple automorphism $\varphi$ of a vertex algebra $V$, the fields in a $\varphi$-twisted $V$-module involve the logarithm of the formal variable, and the action of the Virasoro…

### Orbifold Vertex Operator Algebras and the Positivity Condition

- Mathematics
- 2018

In this note we show that the irreducible twisted modules of a holomorphic, $C_2$-cofinite vertex operator algebra $V$ have $L_0$-weights at least as large as the smallest $L_0$-weight of $V$. Hence,…

### A Cyclic Orbifold Theory for Holomorphic Vertex Operator Algebras and Applications

- Mathematics
- 2016

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…

### Dimension formulae and generalised deep holes of the Leech lattice vertex operator algebra

- MathematicsAnnals of Mathematics
- 2023

We prove a dimension formula for the weight-1 subspace of a vertex operator algebra $V^{\operatorname{orb}(g)}$ obtained by orbifolding a strongly rational, holomorphic vertex operator algebra $V$ of…

### Twisted logarithmic modules of lattice vertex algebras

- MathematicsTransactions of the American Mathematical Society
- 2018

Twisted modules over vertex algebras formalize the relations among twisted vertex operators and have applications to conformal field theory and representation theory. A recent generalization, called…

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

- MathematicsLetters in Mathematical Physics
- 2019

Let L be an even (positive definite) lattice and $$g\in O(L)$$ g ∈ O ( L ) . In this article, we prove that the orbifold vertex operator algebra $$V_{L}^{{\hat{g}}}$$ V L g ^ has group-like fusion if…

### Twisted Logarithmic Modules of Free Field and Lattice Vertex Algebras.

- Mathematics
- 2017

SULLIVAN, STEVEN MCKAY. Twisted Logarithmic Modules of Free Field and Lattice Vertex Algebras. (Under the direction of Bojko Bakalov.) Vertex algebras formalize the relations between vertex operators…

### Extensions of tensor products of Zp-orbifold models of the lattice vertex operator algebra V2Ap−1

- MathematicsJournal of Algebra
- 2018

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