Graded Lie algebras of depth one
The authors prove that an infinite dimensional graded (connected) Lie algebra of depth 1 always contains a free Lie subalgebra on two generators. If X is a simply connected topological space, it is well known that the depth of the rational homotopy Lie algebra of X is less than or equal to the category of X. It results that the rational homotopy Lie algebras of certain spaces contain infinite free Lie subalgebras.
scientific article; zbMATH DE number 4133113