2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112913Thin coverings are a method of constructing graded-simple modules from simple (ungraded) modules. After a general discussion, we classify the thin coverings of (quasifinite) simple modules over associative algebras graded by finite abelian groups. The classification uses the representation theory of cyclotomic quantum tori. We close with an application to representations of multiloop Lie algebras.Representation TheoryRings and Algebras16W50; 17B70text