# 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}
}
• Published 19 February 2004
• Mathematics
• arXiv: Quantum Algebra
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.

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## References

SHOWING 1-10 OF 19 REFERENCES

### Vertex algebras, Kac-Moody algebras, and the Monster.

• R. Borcherds
• Mathematics
Proceedings of the National Academy of Sciences of the United States of America
• 1986
An integral form is constructed for the universal enveloping algebra of any Kac-Moody algebras that can be used to define Kac's groups over finite fields, some new irreducible integrable representations, and a sort of affinization of anyKac-moody algebra.

### Affine Orbifolds and Rational Conformal Field Theory Extensions of W1+∞

• Mathematics
• 1996
Abstract:Chiral orbifold models are defined as gauge field theories with a finite gauge group Γ. We start with a conformal current algebra associated with a connected compact Lie group G and a

### Generalized vertex algebras and relative vertex operators

• Mathematics
• 1993
1. Introduction. 2. The setting. 3. Relative untwisted vertex operators. 4. Quotient vertex operators. 5. A Jacobi identity for relative untwisted vertex operators. 6. Generalized vertex operator

### The operator algebra of orbifold models

• Mathematics
• 1989
We analyze the chiral properties of (orbifold) conformal field theories which are obtained from a given conformal field theory by modding out by a finite symmetry group. For a class of orbifolds, we

### A Unified Conformal Field Theory Description¶of Paired Quantum Hall States

• Mathematics, Physics
• 1999
Abstract:The wave functions of the Haldane–Rezayi paired Hall state have been previously described by a non-unitary conformal field theory with central charge c=−2. Moreover, a relation with the c=1

### Vertex algebras for beginners

Preface. 1: Wightman axioms and vertex algebras. 1.1: Wightman axioms of a QFT. 1.2: d = 2 QFT and chiral algebras. 1.3: Definition of a vertex algebra. 1.4: Holomorphic vertex algebras. 2: Calculus