Lie operad
In mathematics, the Lie operad is an operad whose algebras are Lie algebras. The notion was introduced by in their formulation of Koszul duality.Let denote the free Lie algebra with the generators and the subspace spanned by all the bracket monomials containing each exactly once. The symmetric group acts on by permutations and, under that action, is invariant. Hence, is an operad.
The Koszul-dual of is the commutative-ring operad, an operad whose algebras are commutative rings.
