Editing Lie algebra (section)

== Lie algebra with additional structures ==
A Lie algebra may be equipped with additional structures that are compatible with the Lie bracket. For example, a [[graded Lie algebra]] is a Lie algebra (or more generally a [[Lie superalgebra]]) with a compatible grading. A [[differential graded Lie algebra]] also comes with a differential, making the underlying vector space a [[chain complex]].

For example, the [[homotopy group]]s of a simply connected [[topological space]] form a graded Lie algebra, using the [[Whitehead product]]. In a related construction, [[Daniel Quillen]] used differential graded Lie algebras over the [[rational number]]s <math>\mathbb{Q}</math> to describe [[rational homotopy theory]] in algebraic terms.<ref>{{harvnb|Quillen|1969|loc=Corollary II.6.2.}}</ref>