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math.RA2010★ 4 cited
Free and cofree Hopf algebras
Loïc Foissy
We first prove that a graded, connected, free and cofree Hopf algebra is always self-dual; then that two graded, connected, free and cofree Hopf algebras are isomorphic if, and onl…
math.RA2008★ 2 cited
The infinitesimal Hopf algebra and the poset of planar forests
Loïc Foissy
We introduce an infinitesimal Hopf algebra of planar trees, generalising the construction of the non-commutative Connes-Kreimer Hopf algebra. A non-degenerate pairing and a dual ba…