Pre- and Post-Lie Algebras: The Algebro-Geometric View

  • Gunnar FløystadEmail author
  • Hans Munthe-Kaas
Conference paper
Part of the Abel Symposia book series (ABEL, volume 13)


We relate composition and substitution in pre- and post-Lie algebras to algebraic geometry. The Connes-Kreimer Hopf algebras and MKW Hopf algebras are then coordinate rings of the infinite-dimensional affine varieties consisting of series of trees, resp. Lie series of ordered trees. Furthermore we describe the Hopf algebras which are coordinate rings of the automorphism groups of these varieties, which govern the substitution law in pre- and post-Lie algebras.



We would like to thank Kurusch Ebrahimi-Fard, Kristoffer Føllesdal and Frédéric Patras for discussions on the topics of this paper.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Matematisk InstituttRealfagbyggetBergenNorway

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