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Graftings and cograftings for species
Abstract
We introduce graftings and cograftings for vector species, modelled on the elementary operations of adjoining and deleting a root in a rooted forest. We relate these maps to operads, up and down operators, and obtain nontrivial balanced pairs, admitting pair of creation/annihilation operators with commuting relations. We establish universal properties for the species of rooted forests. Using Fock functors, we recover the classical Connes--Kreimer Hopf algebra, its noncommutative planar analogue, and Foissy's q-infinitesimal Hopf algebra.
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BibTeX
@misc{clavier2026graftings,
title = {{Graftings and cograftings for species}},
author = {Pierre Clavier and Yannic Vargas},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38996},
eprint = {2610.38996},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38996},
}
RIS
TY - UNPB
TI - Graftings and cograftings for species
AU - Pierre Clavier
AU - Yannic Vargas
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38996
UR - https://arxiv.org/abs/2610.38996
AB - We introduce graftings and cograftings for vector species, modelled on the elementary operations of adjoining and deleting a root in a rooted forest. We relate these maps to operads, up and down operators, and obtain nontrivial balanced pairs, admitting pair of creation/annihilation operators with commuting relations. We establish universal properties for the species of rooted forests. Using Fock functors, we recover the classical Connes--Kreimer Hopf algebra, its noncommutative planar analogue, and Foissy's q-infinitesimal Hopf algebra.
ER -