Twisted Modules over Lattice Vertex Algebras

Details Twisted Modules over Lattice Vertex Algebras Twisted Modules over Lattice Vertex Algebras

2004-02-19

arxiv.org/abs/math/0402315v3

in Proc. V Internat. Workshop "Lie Theory and Its Applications in Physics" (Varna, June 2003), eds. H.-D. Doebner and V. K. Do

Mathematics

Quantum Algebra

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

Scientific paper

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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