Twisted Modules over Lattice Vertex Algebras

2004/02/29 by Bojko Bakalov, Victor G. Kac
Mathematics · #math.QA

paper · pdf

published as in Proc. V Internat. Workshop "Lie Theory and Its Applications in Physics" (Varna, June 2003), eds. H.-D. Doebner and V. K. Dobrev, World Scientific, Singapore, 2004. · Dedicated to Professor Ivan Todorov on the occasion of his 70th birthday. 18 pages (references added)

arxiv created 2004/03/31 · arxiv updated 2009/12/01

Abstract

For any integral lattice Q, one can construct a vertex algebra V_Q called a lattice vertex algebra. If σ 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 σ-twisted V_Q-modules. We show that the category of σ-twisted V_Q-modules is a semisimple abelian category with finitely many isomorphism classes of simple objects.

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