2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159081Let K be a compact Lie group. We compute the abelianization of the Lie algebra of equivariant vector fields on a smooth K-manifold X. We also compute the abelianization of the Lie algebra of strata preserving smooth vector fields on the quotient X/K.Minor corrections. To appear in PAMQDifferential GeometryRepresentation Theory22C05, 57R25, 57S15text