2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68659Suppose that $G$ is a locally compact group and $π$ is a (not necessarily irreducible) unitary representation of a closed normal subgroup $N$ of $G$ on a Hilbert space $H$. We extend results of Clifford and Mackey to determine when $π$ extends to a unitary representation of $G$ on the same space $H$ in terms of a cohomological obstruction.Operator AlgebrasRepresentation Theory20C99, 22D10, 22D25, 46L10text