Twisted Modules over Lattice Vertex Algebras

Bojko Bakalov; Victor G. Kac

Twisted Modules over Lattice Vertex Algebras

Quantum Algebra 2007-05-23 v3

Authors: Bojko Bakalov , Victor G. Kac

Abstract

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.

Keywords

vertex operator algebras irreducible modules for lie algebras lie algebras and modules

Cite

@article{arxiv.math/0402315,
  title  = {Twisted Modules over Lattice Vertex Algebras},
  author = {Bojko Bakalov and Victor G. Kac},
  journal= {arXiv preprint arXiv:math/0402315},
  year   = {2007}
}

Comments

Dedicated to Professor Ivan Todorov on the occasion of his 70th birthday. 18 pages (references added)

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