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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.RA2010
Ordered forests and parking functions
Loïc Foissy
We prove that the Hopf algebra of parking functions and the Hopf algebra of ordered forests are isomorphic, using a rigidity theorem for a particular type of bialgebras.
math.RA2010
Left ideals in an enveloping algebra, prelie products and applications to simple complex Lie algebras
Loïc Foissy
We characterize prelie algebras in words of left ideals of the enveloping algebras and in words of modules, and use this result to prove that a simple complex finite-dimensional Li…