On quadri-bialgebras
Quantum Algebra
2020-04-22 v2
Abstract
We introduce the notion of a quadri-bialgebra, which gives a bialgebra theory for the quadri-algebra introduced by Aguiar and Loday. We show that a quadri-bialgebra is equivalent to a Manin triple of dendriform algebras associated to a nondegenerate 2-cocycle, and to a Manin triple of quadri-algebras associated to a nondegenerate invariant bilinear form. Quadri-bialgebras also come from a variation of the classical Yang-Baxter equation, called the -equations. Moreover, quadri-bialgebras fit into the framework of construction of Rota-Baxter operators and Nijenhuis operators on the double spaces of quadri-algebras.
Keywords
Cite
@article{arxiv.1704.04781,
title = {On quadri-bialgebras},
author = {Xiang Ni and Chengming Bai},
journal= {arXiv preprint arXiv:1704.04781},
year = {2020}
}