Differential Graded Lie Algebras and Leibniz Algebra Cohomology

In this note, we interpret Leibniz algebras as differential graded (DG) Lie algebras. Namely, we consider two fully faithful functors from the category of Leibniz algebras to that of DG Lie algebras and show that they naturally give rise to the Leibniz cohomology and the Chevalley-Eilenberg cohomology. As an application, we prove a conjecture stated by Pirashvili in [9].

Automated summary

In this note, Leibniz algebras are interpreted as differential graded (DG) Lie algebras. Two fully faithful functors from the category of Leibniz algebras to that of DG Lie algebras are considered and it is shown that they naturally give rise to the Leibniz cohomology and the Chevalley-Eilenberg cohomology. As an application, a conjecture stated by Pirashvili in [9] is proven.