Deformation of $L_{\infty }$-Algebras

Abstract

In 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 pages