English

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.

Keywords

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