2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76979Let K be a compact Lie group and G its complexification. For a not necessarily reduced Stein K-space X we show that there is a complex space Z endowed with a holomorphic action of the universal complexification G of K that contains X as an open K-stable subset. The correspondence is functorial. As our main result we prove that every coherent K-sheaf on X extends uniquely to a G-sheaf on Z.9 pages, plain texComplex VariablesAlgebraic Geometry32M05text