## Abstract

Rota-Baxter algebras and the closely related dendriform algebras have important physics applications, especially to renormalization of quantum field theory. Braided structures provide effective ways of quantization such as for quantum groups. Continuing recent study relating the two structures, this paper considers Rota-Baxter algebras and dendriform algebras in the braided contexts. Applying the quantum shuffle and quantum quasi-shuffle products, we construct free objects in the categories of braided Rota-Baxter algebras and braided dendriform algebras, under the commutativity condition. We further generalize the notion of dendriform Hopf algebra to the braided context and show that quantum shuffle algebra gives a braided dendriform Hopf algebra. Enveloping braided commutative Rota-Baxter algebras of braided commutative dendriform algebras are obtained.

Original language | English (US) |
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Article number | 2250134 |

Journal | Journal of Algebra and its Applications |

Volume | 21 |

Issue number | 7 |

DOIs | |

State | Published - Jul 1 2022 |

## All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Applied Mathematics

## Keywords

- Quantum shuffle algebra
- Rota-Baxter algebra
- Yang-Baxter equation
- braided Rota-Baxter algebra
- braided dendriform Hopf algebra
- braided dendriform algebra
- dendriform algebra
- quantum quasi-shuffle algebra