Free Pre-Lie Algebras are Free as Lie Algebras
- Autores: Frédéric Chapoton
- Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 53, Nº 3, 2010, págs. 425-437
- Idioma: inglés
- DOI: 10.4153/cmb-2010-063-2
- Enlaces
-
Resumen
We prove that the S-module PreLie is a free Lie algebra in the category of S-modules and can therefore be written as the composition of the S-module Lie with a new S-module X. This implies that free pre-Lie algebras in the category of vector spaces, when considered as Lie algebras, are free on generators that can be described using X. Furthermore, we define a natural filtration on the S-module X. We also obtain a relationship between X and the S-module coming from the anticyclic structure of the PreLie operad.
¿Es nuevo? Regístrese
Ventajas de registrarse
