Eulerian idempotents and Milnor–Moore theorem for certain non-cocommutative Hopf algebras

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Combinatorial Hopf algebras (2008, background): “We will see that they are dendriform bialgebras which have been thoroughly studied in [35, 39, 52, 53, 54].”
On the Lie envelopping algebra of a pre-Lie algebra (2004, background): “Following [5] and [ 20 ], it turns out that the space of planar rooted is a (free) brace algebra.”
Rota–Baxter algebras and dendriform algebras (2005, methodology): “in 1995 with motivation from algebraic K-theory, and was further studied in connection with several areas in mathematics and physics, including operads [54], homology [34, 35], Hopf algebras [13, 47, 58, 65, 32], Lie and Leibniz algebras [35], combinatorics [6, 7, 33, 57], arithmetic [55] and quantu”
On products and duality of binary, quadratic, regular operads (2004, background): “In the next few years, their properties were studied by several authors in areas related to operads [35], homology [17, 18], Hopf algebras [7, 26, 42, 39], combinatorics [16, 37, 2, 3], arithmetic [34] and quantum field theory [16].”
Generalized bialgebras and triples of operads (2006, background): “It includes the case (As,Dipt,MB) and the case (As,Dend, brace) (due to Maŕıa Ronco [76]) which is important since it permits us to unravel the structure of a free brace algebra.”