Lois Pré-Lie En Interaction

Manchon, Dominique; Saidi, Anouar

doi:10.1080/00927872.2010.510813

Cited by 21 publications

(21 citation statements)

References 7 publications

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“…In [CEFM11], D. Calaque, K. Ebrahimi-Fard and D. Manchon introduce a new coproduct, called in this paper the contraction coproduct, on the augmentation ideal of H CK (see also [MS11]).…”

Section: Commutative Casementioning

confidence: 99%

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Preordered forests, packed words and contraction algebras

Mansuy

2014

Journal of Algebra

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We introduce the notions of preordered and heap-preordered forests, generalizing the construction of ordered and heap-ordered forests. We prove that the algebras of preordered and heap-preordered forests are Hopf for the cut coproduct, and we construct a Hopf morphism to the Hopf algebra of packed words. Moreover, we define another coproduct on the preordered forests given by the contraction of edges. Finally, we give a combinatorial description of morphims defined on Hopf algebras of forests with values in the Hopf algebras of shuffes or quasi-shuffles.Résumé. Nous introduisons les notions de forêts préordonnées et préordonnées en tas, généralisant les constructions des forêts ordonnées et ordonnées en tas. On démontre que les algèbres des forêts préordonnées et préordonnées en tas sont des algèbres de Hopf pour le coproduit de coupes et on construit un morphisme d'algèbres de Hopf dans l'algèbre des mots tassés. D'autre part, nous définissons un autre coproduit sur les forêts préordonnées donné par la contraction d'arêtes. Enfin, nous donnons une description combinatoire de morphismes définis sur des algèbres de Hopf de forêts et à valeurs dans les algèbres de Hopf de battages et de battages contractants.

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“…In [CEFM11], D. Calaque, K. Ebrahimi-Fard and D. Manchon introduce a new coproduct, called in this paper the contraction coproduct, on the augmentation ideal of H CK (see also [MS11]).…”

Section: Commutative Casementioning

confidence: 99%

“…Afterwards, we study a another coproduct called in this paper the contraction coproduct. In [CEFM11], D. Calaque, K. Ebrahimi-Fard and D. Manchon define this coproduct in a commutative case, on a quotient C CK of H CK (see also [MS11]). We give a decorated version C D CK of C CK .…”

Section: Introductionmentioning

confidence: 99%

Preordered forests, packed words and contraction algebras

Mansuy

2014

Journal of Algebra

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“…Remark 7. -The partial compositions defined above give rise to two right pre-Lie structures ⊳ and ← on F P L [4], the first acting on the second by derivation [19]. The pre-Lie structure ← is defined by:…”

Section: Two Operads Of Rooted Trees: Pre-lie and Napmentioning

confidence: 99%

The Pre-Lie Operad as a Deformation of Nap

Saidi

2013

J. Algebra Appl.

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“…The pre-Lie operation (s, t) → (s ← t) is given by the sum of the graftings of t on s at all vertices of s. As a consequence of (29) we have two pre-Lie operations on T = n≥2 T n which interact as follows [27]:…”

Section: 1mentioning

confidence: 99%

“…Following [9] and [7] we recall the construction of the group associated to any augmented operad as well as the associated pre-Lie algebra, and we recall the description of the free pre-Lie algebra in terms of rooted trees. As an application we describe a second pre-Lie algebra product on rooted trees which acts on the first by derivations [4], [27]. The third part is devoted to pre-Lie algebras of vector fields on R n , from the work of A. Cayley [5] to modern developments in numerical analysis through B-series [3], [21], [26], [11].…”

Section: Introductionmentioning

confidence: 99%