The bigraft algebras
Rings and Algebras
2012-06-26 v1
Abstract
In this paper, we introduce the notion of bigraft algebra, generalizing the notions of left and right graft algebras. We give a combinatorial description of the free bigraft algebra generated by one generator and we endow this algebra with a Hopf algebra structure, and a pairing. Next, we study the Koszul dual of the bigraft operad and we give a combinatorial description of the free dual bigraft algebra generated by one generator. With the help of a rewriting method, we prove that the bigraft operad is Koszul. Finally, we define the notion of infinitesimal bigraft bialgebra and we prove a rigidity theorem for connected infinitesimal bigraft bialgebras.
Cite
@article{arxiv.1206.5590,
title = {The bigraft algebras},
author = {Anthony Mansuy},
journal= {arXiv preprint arXiv:1206.5590},
year = {2012}
}
Comments
45 pages. arXiv admin note: text overlap with arXiv:1007.1547