Representations and cohomologies of differential 3-Lie algebras with any weight and applications

Abstract

The purpose of this paper is to study cohomologies of differential [Formula: see text]-Lie algebras with any weight and applications. First, we introduce representations of differential [Formula: see text]-Lie algebras. Moreover, we develop cohomology theory of differential [Formula: see text]-Lie algebras. We also depict the relationship between the cohomologies of a differential [Formula: see text]-Lie algebra and its associated differential Leibniz algebra with weight zero. Finally, formal deformations, abelian extensions and skeletal differential [Formula: see text]-Lie 2-algebras are characterized in terms of cohomology groups.