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arXiv · 1704.06171

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

Gunnar Fløystad·Hans Munthe-Kaas
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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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Gunnar Fløystad, Hans Munthe-Kaas. 2017-04-20. Pre- and Post-Lie Algebras: The Algebro-Geometric View. https://arxiv.org/abs/1704.06171

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