Free pre-Lie algebras are free as Lie algebras

Abstract

We prove that free pre-Lie algebras, when considered as Lie algebras, are free. Working in the category of S-modules, we define a natural filtration on the space of generators. We also relate the symmetric group action on generators with the structure of the anticyclic PreLie operad.

14 pages

References in corpus (1)

• On some anticyclic operads

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