2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/226722We compare two combinatorial definitions of parabolic sets of roots. We show that these definitions are equivalent for simple finite dimensional Lie algebras, affine Lie algebras, and toroidal Lie algebras. In contrast, these definitions are not always equivalent for simple finite dimensional Lie superalgebras.added remarkRepresentation TheoryRings and Algebras17B20; 17B65; 17B67text