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The Abel Symposium

Abelsymposium 2016: Computation and Combinatorics in Dynamics, Stochastics and Control pp 321–367Cite as

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

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Part of the book series: Abel Symposia ((ABEL,volume 13))

Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Matematisk Institutt, Realfagbygget, Bergen, Norway

    Gunnar Fløystad & Hans Munthe-Kaas

Authors
  1. Gunnar Fløystad
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  2. Hans Munthe-Kaas
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Corresponding author

Correspondence to Gunnar Fløystad .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

    Elena Celledoni

  2. Department of Mathematics, University of Oslo, Oslo, Norway

    Giulia Di Nunno

  3. Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

    Kurusch Ebrahimi-Fard

  4. Department of Mathematics, University of Bergen, Bergen, Norway

    Hans Zanna Munthe-Kaas

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Fløystad, G., Munthe-Kaas, H. (2018). Pre- and Post-Lie Algebras: The Algebro-Geometric View. In: Celledoni, E., Di Nunno, G., Ebrahimi-Fard, K., Munthe-Kaas, H. (eds) Computation and Combinatorics in Dynamics, Stochastics and Control. Abelsymposium 2016. Abel Symposia, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-030-01593-0_12

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