Classification of 2-term $L_{\infty }$-algebras

Abstract

We classify all 2-term $L_{\infty }$-algebras up to isomorphism. We show that such $L_{\infty }$-algebras are classified by a Lie algebra, a vector space, a representation (all up to isomorphism) and a cohomology class of the corresponding Lie algebra cohomology.

16 pages