TY - JOUR

T1 - Braided Rota-Baxter algebras, quantum quasi-shuffle algebras and braided dendriform algebras

AU - Li, Yunnan

AU - Guo, Li

N1 - Funding Information:
This work is supported by the NSFC Grants (Nos. 12071094, 11771142, 11771190) and the China Scholarship Council (No. 201808440068). Y. Li also thanks Rutgers University at Newark for providing a stimulating environment of research during his visit from August 2018 to August 2019. The authors thank the referee for helpful suggestions.
Publisher Copyright:
© 2022 World Scientific Publishing Company.

PY - 2022/7/1

Y1 - 2022/7/1

N2 - 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.

AB - 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.

KW - Quantum shuffle algebra

KW - Rota-Baxter algebra

KW - Yang-Baxter equation

KW - braided Rota-Baxter algebra

KW - braided dendriform Hopf algebra

KW - braided dendriform algebra

KW - dendriform algebra

KW - quantum quasi-shuffle algebra

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U2 - 10.1142/S0219498822501341

DO - 10.1142/S0219498822501341

M3 - Article

AN - SCOPUS:85103880275

SN - 0219-4988

VL - 21

JO - Journal of Algebra and Its Applications

JF - Journal of Algebra and Its Applications

IS - 7

M1 - 2250134

ER -