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The Cartier-Quillen-Milnor-Moore theorem in the Post-Hopf case

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arxiv 2401.09116 v3 pith:BR2TWYWN submitted 2024-01-17 math.CO math.RA

Pierre Catoire (IMAG) This is my paper · ORCID
classification math.COmath.RA
keywords algebraspost-hopfpost-liecartier-quillen-milnor-mooredescriptiongiveleftright
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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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  1. An infinitesimal deformation of the post-Lie and post-Hopf algebra correspondence

    math.QA 2026-07 accept novelty 6.0 of 10

    Infinitesimal post-Lie/post-Hopf structures preserve the U⊣P adjunction and yield a Cartier–Milnor–Moore equivalence, with classifications on sl(2) and H4 and Koszulity of the IPL operad.

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