2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71319In this paper, deformations of $L_\infty$-algebras are defined in such a way that the bases of deformations are $L_\infty$-algebras, as well. A universal and a semiuniversal deformation is constructed for $L_\infty$-algebras, whose cotangent complex admits a splitting. The paper also contains an explicit construction of a minimal $L_\infty$-structure on the homology $H$ of a differential graded Lie algebra $L$ and of an $L_\infty$-quasi-isomorphism between $H$ and $L$.29 pagesQuantum Algebra13D10; 14B20text