On the Lie envelopping algebra of a preLie algebra
Abstract
We construct an associative product on the symmetric module S(L) of any preLie algebra L. Then we proove that in the case of rooted trees our construction is dual to that of Connes and Kreimer. We also show that symmetric brace algebras and preLie algebras are the same. Finally, using brace algebras instead of preLie algebras, we give a similar interpretation of Foissy's Hopf algebra of planar rooted trees.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2004
 arXiv:
 arXiv:math/0404457
 Bibcode:
 2004math......4457O
 Keywords:

 Quantum Algebra;
 16W30;
 16S30;
 17B35;
 05C05