Twisted Modules over Lattice Vertex Algebras

By B. Bakalov, V. Kac. 2004

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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.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/80b463a5f9dd26f5d43c994ecf2610ecdbda1a1e