Classification of irreducible modules of the vertex algebra $V_L^+$ when $L$ is a nondegenerate even lattice of an arbitrary rank

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164300In this paper, we first classify all irreducible modules of the vertex algebra $V_L^+$ when $L$ is a negative definite even lattice of arbitrary rank. In particular, we show that any irreducible $V_L^+$-module is isomorphic to a submodule of an irreducible twisted $V_L$-module. We then extend this result to a vertex algebra $V_L^+$ when $L$ is a nondegenerate even lattice of finite rank.To appear in J. of AlgebraQuantum AlgebraClassification of irreducible modules of the vertex algebra $V_L^+$ when $L$ is a nondegenerate even lattice of an arbitrary ranktext