2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72829In this paper,we will show how to kill the obstructions to Lie algebra deformations via a method which essentially embeds a Lie algebra into Strong homotopy Lie algebra or $L_{\infty}$ algebra. All such obstructions have been transfered to the revelvant $L_{\infty}$ algebras which contain only three termsQuantum AlgebraAlgebraic Topology$L_{\infty}$ algebra structures of Lie algebra deformationstext