2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112830A Bernstein-Gelfand-Gelfand resolution for arbitrary Kac-Moody algebras and arbitrary subsets of the set of simple roots is proven. Moreover, quantum group analogs of the Bernstein-Gelfand-Gelfand resolution for symmetrizable Kac-Moody algebras are established. For quantized enveloping algebras with fixed complex nonzero deformation parameter q exactness is proven for all q which are not a root of unity.12 pagesQuantum Algebra17B67; 17B37text