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Deformation of $L_\infty$-Algebras

Frank Schuhmacher
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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 $L$.

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Frank Schuhmacher. 2004-05-26. Deformation of $L_\infty$-Algebras. https://arxiv.org/abs/math/0405485

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