For questions about differential graded Lie algebras.
A differential graded Lie algebra, or dg Lie algebra, is a Lie algebra $\mathfrak{g}$ that has the structure of a graded vector space $\mathfrak{g} = \bigoplus \mathfrak{g}_i$ such that the Lie bracket "respects that grading" and such that there exists a differential map defined on $\mathfrak{g}$. Details can be found on the Wikipedia page.