The symmetric operation in a free pre-Lie algebra is magmatic

Details The symmetric operation in a free pre-Lie algebra is magmatic The symmetric operation in a free pre-Lie algebra is magmatic

2010-04-07

arxiv.org/abs/1004.1204v3

Proc. Amer. Math. Soc. 139-5 (2011), 1585-1597

Mathematics

Rings and Algebras

View in color, 12 pages

Scientific paper

A pre-Lie product is a binary operation whose associator is symmetric in the last two variables. As a consequence its antisymmetrization is a Lie bracket. In this paper we study the symmetrization of the pre-Lie product. We show that it does not satisfy any other universal relation than commutativity. It means that the map from the free commutative-magmatic algebra to the free pre-Lie algebra induced by the symmetrization of the pre-Lie product is injective. This result is in contrast with the associative case, where the symmetrization gives rise to the notion of Jordan algebra. We first give a self-contained proof. Then we give a proof which uses the properties of dendriform and duplicial algebras.

Affiliated with

Also associated with

No associations

Rating

The symmetric operation in a free pre-Lie algebra is magmatic does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The symmetric operation in a free pre-Lie algebra is magmatic, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The symmetric operation in a free pre-Lie algebra is magmatic will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-712836