2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65682In this article, we study module categries of simple current extensions of vertex operator algebras. Under certain assumptions, we show that every module for a rational vertex operator algebra be lifted to a twisted module for an extended algebra with an abelian symmetry.latex 14 pages, version 2: English corrected, version 3: Hypotheis I is proved in Lemma 3.1Quantum Algebra17B69text