On the Lie enveloping algebra of a pre-Lie algebra
- 28 May 2008
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of K-theory
- Vol. 2 (1) , 147-167
Abstract
We construct an associative product on the symmetric module S(L) of any pre-Lie algebra L. It turns S(L) into a Hopf algebra which is isomorphic to the enveloping algebra of LLie. Then we prove that in the case of rooted trees our construction gives the Grossman-Larson Hopf algebra, which is known to be the dual of the Connes-Kreimer Hopf algebra. We also show that symmetric brace algebras and pre-Lie algebras are the same. Finally, we give a similar interpretation of the Hopf algebra of planar rooted trees.Keywords
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