For graded post-Lie structures on free Lie algebras, the coproduct dual to the Grossman-Larson product is given explicitly, yielding new dual Hopf algebra descriptions for the Ihara and ari brackets and a conjectural post-Lie model for the uri bracket.
The Cartier-Quillen-Milnor-Moore theorem in the Post-Hopf case
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abstract
We give the definition of left/right Post-Lie algebras and left/right Post-Hopf algebras and establish a link between those objects. We get a Cartier-Quillen-Milnor-Moore theorem for Post-Hopf algebras. We give another description for free Post-Lie algebras and a description for Post-Lie algebras obtained from an associative product.
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On post-Lie structures for free Lie algebras
For graded post-Lie structures on free Lie algebras, the coproduct dual to the Grossman-Larson product is given explicitly, yielding new dual Hopf algebra descriptions for the Ihara and ari brackets and a conjectural post-Lie model for the uri bracket.