Manin triples of post-Lie algebras with invariant bilinear form are shown to be equivalent to pp-post-Lie bialgebras, yielding a bialgebra theory for post-Lie algebras.
Aguiar, Infinitesimal Hopf algebras
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A bialgebra theory of post-Lie algebras via Manin triples and generalized Hessian Lie groups
Manin triples of post-Lie algebras with invariant bilinear form are shown to be equivalent to pp-post-Lie bialgebras, yielding a bialgebra theory for post-Lie algebras.