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

Abstract

The purpose of the present paper is to study cohomologies of differential 3-Lie algebras with any weight. We introduce the representation of a differential 3-Lie algebra. Moreover, we develop cohomology theory of a differential 3-Lie algebra. We also depict the relationship between the cohomologies of a differential 3-Lie algebra and its associated differential Leibniz algebra with weight zero. Formal deformations, abelian extensions and skeletal differential 3-Lie 2-algebras are characterized in terms of cohomology groups

Deformations and Extensions of Modified λ-Differential 3-Lie Algebras

“…In recent years, scholars have increasingly focused on structures with arbitrary weights, thanks to the important work of [32][33][34][35][36][37]. The papers [38][39][40] established the cohomology, extensions and deformations of Rota-Baxter 3-Lie algebras with any weight λ, as well as the differential 3-Lie algebras with any weight λ. Additionally, the cohomology and deformation of modified Rota-Baxter algebras were studied by Das [41]. The works [42,43] provided insights into the cohomology and deformation of modified Rota-Baxter Leibniz algebras with weight λ.…”