On the Lie envelopping algebra of a pre-Lie algebra

By Jean-Michel Oudom, D. Guin. 2004

141 citations recorded by the source corpus.

We construct an associative product on the symmetric module S(L) of any pre-Lie 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 pre-Lie algebras are the same. Finally, using brace algebras instead of pre-Lie algebras, we give a similar interpretation of Foissy's Hopf algebra of planar rooted trees.

Subfields: Algebra and Number Theory, Geometry and Topology, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/a361695a6c9a0e6d8cca11213134b1f515560fe3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Vladimir Dotsenko
2. Chengming Bai
3. Sergey Shadrin
4. Y. Sheng
5. Rong Tang
6. Li Guo
7. Bruno Vallette
8. Jean-Louis Loday

In Geometry and Topology

1. Vladimir Dotsenko
2. Chengming Bai
3. Sergey Shadrin
4. Y. Sheng
5. Li Guo
6. Rong Tang
7. Bruno Vallette
8. Jean-Louis Loday

In Molecular Biology

1. Sergey Shadrin
2. Vladimir Dotsenko
3. Bruno Vallette

Citations in the corpus

• Post-groups, (Lie-)Butcher groups and the Yang–Baxter equation (2023, background): “See [22, 36, 39, 45] for more studies on the universal enveloping algebras of post-Lie algebras.”
• On the Lie Enveloping Algebra of a Post-Lie Algebra (2014, unknown): “The remainder of this section contains statements and some proofs analogous to the ones in [27, Section 2], slightly modified to match our setting.”
• Pre-Lie deformation theory (2015, background): “Recall that one can associate to any pre-Lie product an infinite collection of operations of any arity, called the symmetric braces , see [OG08, LM05].”