Bialgebra and Hopf algebra structures on free Rota-Baxter algebras
Rings and Algebras
2016-04-13 v1 Quantum Algebra
Abstract
In this paper, we obtain a canonical factorization of basis elements in free Rota-Baxter algebras built on bracketed words. This canonical factorization is applied to give a coalgebra structure on the free Rota-Baxter algebras. Together with the Rota-Baxter algebra multiplication, this coproduct gives a bialgebra structure on the free Rota-Baxter algebra of rooted forests. When the weight of the Rota-Baxter algebra is zero, we further obtain a Hopf algebra structure.
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Cite
@article{arxiv.1604.03238,
title = {Bialgebra and Hopf algebra structures on free Rota-Baxter algebras},
author = {Xing Gao and Li Guo and Tianjie Zhang},
journal= {arXiv preprint arXiv:1604.03238},
year = {2016}
}
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17 pages