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

TL;DR

This paper provides a complete classification of 2-term $L_$-algebras, showing they are characterized by a Lie algebra, a vector space, a representation, and a cohomology class, up to isomorphism.

Contribution

It offers a comprehensive classification of 2-term $L_$-algebras using Lie algebra data and cohomology, extending previous understanding of these algebraic structures.

Findings

Classification by Lie algebra, vector space, representation, and cohomology class

All 2-term $L_$-algebras are classified up to isomorphism

Provides explicit correspondence between algebraic data and $L_$-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.