Doubling pre-Lie algebra of rooted trees

@article{BelhajMohamed2019DoublingPA,
  title={Doubling pre-Lie algebra of rooted trees},
  author={Mohamed Belhaj Mohamed},
  journal={Journal of Algebra and Its Applications},
  year={2019}
}
We study the pre-Lie algebra of rooted trees [Formula: see text] and we define a pre-Lie structure on its doubling space [Formula: see text]. Also, we find the enveloping algebras of the two pre-Lie algebras denoted, respectively, by [Formula: see text] and [Formula: see text]. We prove that [Formula: see text] is a module-bialgebra on [Formula: see text] and we find some relations between the two pre-Lie structures. 

References

SHOWING 1-10 OF 21 REFERENCES

On the Lie envelopping algebra of a pre-Lie algebra

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

Pre-Lie algebras and the rooted trees operad

A Pre-Lie algebra is a vector space L endowed with a bilinear product * : L \times L to L satisfying the relation (x*y)*z-x*(y*z)= (x*z)*y-x*(z*y), for all x,y,z in L. We give an explicit

Hopf-algebraic structure of families of trees

Doubling bialgebras of rooted trees

The vector space spanned by rooted forests admits two graded bialgebra structures. The first is defined by Connes and Kreimer using admissible cuts, and the second is defined by Calaque,

Combinatorial Hopf algebras

We define a "combinatorial Hopf algebra" as a Hopf algebra which is free (or cofree) and equipped with a given isomorphism to the free algebra over the indecomposables (resp. the cofree coalgebra

Left-symmetric algebras, or pre-Lie algebras in geometry and physics

In this survey article we discuss the origin, theory and applications of left-symmetric algebras (LSAs in short) in geometry in physics. Recently Connes, Kreimer and Kontsevich have introduced LSAs

Renormalization in Quantum Field Theory and the Riemann–Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem

Abstract:This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedure

A short survey on pre-Lie algebras

We give an account of fundamental properties of pre-Lie algebras, and provide several examples borrowed from various domains of Mathematics and Physics : Algebra, Combinatorics, Quantum Field Theory